Would giving dwarves specific racial proficiencies instead of Weapon Familiarity be unbalanced?

No, there is nothing game breaking about it

Proficiencies are usually the mínimo powerful ability on a class/race combination's toolkit, and we see those being handed-out all the time in player options such as feats, sub-classes, sub-races. It's not uncommon to see a variant rule in a sourcebook that says "replace this feature by this another feature", or something along the lines of "dwarven tunnel druids are proficient with dwarven waraxes and warhammers".

So it's fine really, if the GM and the players agree, you can modify small rules without any major consequence in the gameplay in the long run.

Note that, even though only a small advantage, the character now tem an advantage. Some GM's are not okay with that and would like to take something away to make up for it, or (at least) give this same treatment to the other players, or maybe even to the NPCs, making this change be balanced across the board as todo o mundo has it now. That is also fine, and should be discussed between the player(s) what would be a solution that works best for everybody.

Dê uma olhada na variant races list and see if there is anything that comes to your attention. For instance, Earth Dwarves have a stronger perception to notice unusual stonecutting, but lose their +1 attack against orcs and goblinoids, among other things. Desert Dwarves have no racial bonus on Craft checks, and instead of combat bonuses against goblinoids, they get it against reptilian races.

Druids can’t really use weapon familiarity, while they can use weapon proficiency, so on some level you’re giving the character “something for nothing.”

On the other hand, a dwarven fighter would have exactly the opposite position, having no use for weapon proficiency she already has from her class, while the weapon familiarity could potentially allow her to use weapons she otherwise couldn’t.

Ultimately, classes that lack martial weapon proficiency usually aren’t expected to make a lot of weapon attacks. The only real exception I can think of is a cleric. Druids often make a lot of attacks—but with tooth and claw, not weapons. Since wild shape replaces a druid’s physical ability scores, they often have low Strength and/or Dexterity in their regular form. If they do, then they won’t be very good at weapon attacks. If they choose to get more Strength, then they are sacrificing a major benefit of the druid class.

Similar arguments can be made for most of the classes without martial weapon proficiency.

So I tend to think that weapon familiarity is the more powerful feature, at least in theory. Dwarven weapons available that way are pretty poor—as, indeed, exotic weapons often are—but at least those who benefit (those who have martial weapon proficiency) are those who are likely to use it (likely to make weapon attacks as a major focus).

In short, yeah, trading weapon familiarity in some exotic weapons for weapon proficiency in some martial weapons is probably fine in general, and certainly seems like no problem for a druid. A dwarven cleric might be more of a concern, but ultimately both weapon familiarity and weapon proficiency are both realmente low-value features, so I wouldn’t be overly concerned about it even then. Ultimately, either of these amounts to an average damage roll just +1 greater than without it, for the appropriate classes. Even at 1st level, 1 damage is a paltry amount. It swiftly degrades in value as levels are accrued. Really, the only martial weapons that offer a significant improvement over simple weapons are the bows—you know, the ones that elves are já offering racial proficiency in.

Yes, it can be game-breaking - not because getting a bit stronger than combat is so strong, but because the Druid is already so powerful to begin with in 3.X edition.

Full caster classes (Druid included) are already the strongest classes in the game. By giving them additional weapon proficiencies, you're just removing one of their few weaknesses, and thereby making them even more versatile and thus powerful than they already are.

I mean, he's playing a Druid. There's a reason why the term "CoDzilla" came into being to describe straight Cleric or Druid builds. It's entirely possible that his animal companion is a better fighter than the Fighter is! He doesn't need extra weapon proficiencies.