Explain it to them just as you explained it to us:
"It makes me uncomfortable and I believe it will make the other players uncomfortable." is a perfectly valid reason to veto a character.

It also may be worth telling them to prepare another character "just in case" and bring up their character concept in session zero, the other players may be OK with it, exploring things in a game that would not be acceptable in the real world can often be fun depending on how the player handles it. You can say "If the other players are OK with it I will allow it for not but if you push it too far and it makes anyone (including you) uncomfortable then the character leaves and you bring in your spare, no questions asked".

Other players may be fine with it, this may be affected by how "real" they play the bigotry and how real the setting is, a Caricature can be fun. I myself had a lot of fun playing a racist (clade-ist?) lizardfolk who just did not like mammals "You all have things hanging off you", (genitalia, breasts, hair) "and you're always leaking fluids, it's just weird.". He still saved the world with a group of mammals and the other players had fun with it as well, especially because he was fine killing (and eating) mammalian humanoids but went to extraordinary lengths to not harm intelligent reptilian enemies. The fact he was a bit monstrous (seriously he ate like a dozen people throughout the campaign) made it more fun and unreal enough to not be uncomfortable. But I also talked it over with all the other players at session zero to make sure they were fine with it beforehand; these were players who knew me and knew I was just playing a monster.

Talk to the Player-- Privately, Politely, Firmly, and Pre-Emptively

This is not something I've faced directly, in the sense of a homophobic character, but I have faced it with misogynistic players/characters, and I think what I learned carries over well.

I don't know your player, so I will bend over backward to give him the benefit of the doubt and assume that he's just aiming for gritty realism and edgy dramatic conflicts, rather than actually espousing any of this himself.

But after bending over backward... I find it doesn't matter. I'd still talk to the player and explain that this isn't acceptable and you'd like him to modify the character. I think the words you've already chosen to describe the situation to us are great starting points (with a minor caveat; see below.)

• My limit for the number of players at the table made seriously uncomfortable by another player (including the portrayal of his PC) is zero. Really, it's as simple as that. Zero. Just don't do it at my table. I will also err on the side of caution, here, especially with matters of sexuality, race, and religion, for a variety of reasons that I can best briefly articulate as, "This person deals with this in real life o tempo todo. I will not insist that they deal with it from other players in a recreational activity."

  (Adding "seriously" to uncomfortable may give it a weaselly quality that I don't intend. I intend it mainly as a hedge to prevent spurious objections. Someone, at some point, will need to be an authority and as the GM that person is ultimately you.)

• The GM-- in this case, you-- is a player. You count.

If you were just a player, not the GM, I would urge you to go to the GM or, less probably, to the group as a whole. Since you are the GM, as long as you're acting in good faith, you certainly pode go to the group and have a group discussion, but I don't think it's necessary. As long as you're acting in good faith, you can act on your own behalf.

The only caveat I have is that I probably would not bring up other players' reactions to the character unless I had explicitly cleared it with them (or they were part of the conversation.) No one like to have words put in their mouth.

In the best outcome, the player will say, "Oh, okay, I didn't think about it that way," change the character, and life goes on. No one else even needs to know about it. But occasionally you'll find someone a lot more attached to this sort of thing than you expected. That's where you have to decide how much "My way or the highway" you can enforce.

Consider for a minute that role playing games are largely based on the concept of allowing players to act out dangerous, scary, and/or heroic situations in a safe environment.

RPGs are often filled with things that would absolutely terrify us if they happened in real life - walking around in a world filled with violence, magic, Big Bad Guys, death, combat, intrigue, subversion, and just general conflict. Players get to act out scenarios and describe how they would deal with these monumental challenges, without actually putting themselves at risk.

As a very basic example, your character walks into a situation or a scene, is faced by a group of scary beings holding weapons. In real life, that would be utterly terrifying. But it's a core part of the game!

As a less obvious example, an NPC that has befriended your party is being deceptive and undermining your ultimate goal by helping your enemy. That would never be something I would choose to face in real life, but again - it adds to the game, and story elements that present challenges are a key part of why it's interesting.

Ultimately, the people involved in a particular game must be able to discuss freely and decide what is or is not acceptable. But consider this - I've played in many D&D games that involved things that are scary to me, personally. In effect, that's part of the fun - I get to work through how I would handle these things. I get to confront them mentalmente which can, in a sense, help me work through how I feel about them. I'm sure this is a common experience for many people who play RPGs, it just probably happens around things that are less obvious than homophobia.

Let's put this in context for your question.

In real life, a homophobic Russian might be frightening to you. But I'm sure there are many other scary things happening in your game, which add value to the story. Many of them may be purely fantasy-based, but some of them may closely echo things that actually happen in the real world (conflict between friends, people who try to manipulate you, and so on). Consider if this idea, too, can add value. Maybe the character's homophobia will somehow hinder his progress. Maybe he will have a change of heart because he experiences something that really shakes his core beliefs. Maybe he will somehow "win" in the end, by some trick of fate, in a way that actually somehow reinforces his beliefs.

So - before discarding something because it's frightening, consider:

• Talking through the concept with the player. Understanding why he wants to include this element, and how he intends to act it out. Make sure it is clear among everyone that there is a separation between the real player in the real world, and the actions their character takes in the game world.
• Talking through how this element may, or may not, fit with the overall plot you have in mind as DM.
• Doing a gut check with other players to make sure they're comfortable with the idea.

I know these steps aren't significantly different than the content of other answers, but I am hoping I can offer a different perspective on why you might want to do these things versus just immediately discarding the idea.

You do what you should always do in a situation where there is potential conflict between the participants (including the GM): you get the group together and you talk about the issue and the boundaries you want to set, entirely out of character. There are a number of possibilities which could come out of the discussion:

1. You all agree that having a homophobic character is OK, but there are certain lines which should not be crossed.
2. The player agrees to remove the homophobic aspect of his character, or to play a different character entirely.
3. You can't come to a solution as a group, so you decide to do the campaign without that player.
4. You can't come to a solution as a group, so the group decides to play this campaign without you as GM.

Particularly in case 1 it is wise to establish a system of "OK" checks which enable any participant to pause the in character game and discuss issues or of character. That's not a bad idea for any game, but it's particularly important if you know your game may approach boundaries that make people uncomfortable or worse.

The already-posted answers are great, but there hasn't been much focus on what actual play with the PC would be like. I see three very broad categories to consider, and if the answers you and your player come up with for these aren't satisfying then not allowing this PC makes sense:

1. Does this campaign offer scope for this?

If your campaign is filled with PCs and NPCs where their sexual orientation just isn't an issue, because people haven't fleshed that detail of the characters out or it isn't really something that happens on-camera, then this character detail might be totally irrelevant.

So, does this player esperar to have chances to vent their PC's prejudices? Are they assuming that you will insert conflicts to explore that aspect of the character? Or is it more of an idle trait, something where they'll know how to act if it comes up but they aren't necessarily expecting the issue to come up?

2. What is the player expecting to get out of this trait?

Sometimes players come up with themes they'd like to explore in-game, sometimes they're looking for a more cosmetic feature, and sometimes they're looking for a fig leaf that will allow them to say and do things they feel like saying and doing.

I'm generally more open to players introducing potentially awkward or difficult things as long as they add some substance to the game. A player whose character just wants to offend modern sensibilities is likely to find their choice forbidden at the outset or facing extreme in-game difficulties as a result of their chosen conduct.

3. How will this play out at the table?

This is the most important one, and will require some discussion between you and this player (if not all of your players). If this player wants to say homophobic things at the table (whether obviously, completely in character or not), I would be a lot less likely to allow it. Simply reciting known invectives adds little to the game or character, and can easily be both offensive and shallow.

On the other hand, I've found abstracting this kind of thing to narrative description or, better still, dice rolls and modifiers to be really productive and interesting. Because I personally find the situations (and outcomes) that prejudiced characters tend to provoke fairly interesting, it's easy enough to skip the actual prejudiced comments.

• If this PC is obsessed with NPCs' sexual orientations, they can consent to social skill checks when they meet new characters to try to figure out if they should behave horribly or not (or have those checks imposed on them).
• Their prejudices might manifest not only as explicit comments but as a stat modifier for interactions (if they can't stifle their prejudice, maybe they suffer a -2 on CHA checks with characters that offend them).
• They can have a roll representing self control to avoid displaying their homophobia, with negative consequences for failures.

There are lots of other possibilities, too. I've used the narrative-abstraction-and-dice technique for things I didn't want to play out explicitly. Most notably, I used it for a PC seducing an NPC. I really didn't want to RP out sex between them, but the abstract descriptions and rolls allowed for the PC to behave as they wanted, for their behavior to affect the game world in a plausible way, and no one had to deal with potential discomfort from the explicit material.

Start with Session 0

There are a ton of good resources about Session 0, and new ones keep being created.

Sessão 0

Basically, before you play your first game everyone gets together and talks about the campaign in general. What kind of characters is everyone going to play? (often having everyone make characters together at Session 0 can be a big benefit). What sort of tone, theme, and setting is the campaign going to take (slapstick? Grimdark Fantasy? Low Magic but otherwise High Fantasy? Urban intrigue?)? What sort of things do people want to see or avoid in the campaign?

A few resources I do think are worth highlighting:

• Consent in Gaming This just came out a couple weeks ago and consolidates a bunch of resources such as Lines & Veils e The X Card which can make games more comfortable for everyone. In particular this might be useful to you.
• What is Session 0 Oh look, it's another question on this site.
• Ferramenta Mesma Página This can often be handled before Session 0 if everyone is connected online.
• Geek & Sundry has a broad article about the usefulness of session 0.

Keep in mind this is a small selection of the tools that exist, not an exhaustive list. Don't be afraid to use your favorite search engine to look for more.

Don’t talk to us - talk to him

It’s your (as in all of you) role-playing game and no one outside your group has a justifiable reason for telling you that this or that area of human experience is off-limits for you to explore. However, each and everyone of you dentro the social group has an unarguable right to have their own limits and to raise objections when those limits are violated.

Raise your concerns and let others raise theirs - you may be right that they will “probably” feel the same way but you should let them speak for themselves.

Now I’ve known this player for a long time and I know he isn’t the type to throw out offensive slurs, but even then, as a bisexual this makes me uncomfortable.

To be honest, if you're certo that the player is not homophobic, that they do not think like that and have no reason to do it just to annoy you (or rub it into your face or anything like that), I fail to see the problem. Sure, it might make people uncomfortable for valid reasons, but if it is not directed at them in any way but at their characters, it should be treated as such, namely as something inside the game.

I like playing characters which move me outside of my comfort zone, as it broadens my horizon and makes me as a person grow. I also like to play with other characters which do the same to me, because that also makes me grow as a person. Also I like to see how characters develop over time. Ask them why they want to play that character, maybe they just want to explore such a character for a little and so what happens. Example, I'm currently preparing to play a mage who has no problem with sacrificing people and using them as subjects for experiments (involuntarily, of course). That is my premise, and I'm very, very curious to see two things. First, how the others handle such a character. Second, how that character evolves with time. There is a good chance that I will give in at some point and just become one of the good guys, but there's also a good chance that I will, sooner or later, poison all the others. That doesn't mean that I hate the other players, far from it, but I'm curious how that character will behave, develop and evolve.

On the other side, if you have any reason to believe that they do it to annoy you in any way...you don't have a problem with the character, you should evaluate your social status with that person.

Ultimately, as others have said, talk with them, ask them why, and see where that takes you.

Another thing to consider is the story arc the character is trying to achieve. Is the character arc a homophobic PC being challenged and having their views changed or just a homophobe with no redemption? This could make a difference in how comfortable the rest of the table is in accommodating them.