Realistically it comes down to revenge and self preservation
Vingança
Would you shake hands with Bob after he sold a weapon to Murderous Ted, after Ted specially said he was going to kill your best friend and Bob gave it to him anyway knowing that Ted was capable of killing your best friend?
If you answer yes it is not even slightly Bob's fault in your mind then congratulations... you can be the next Mother Teresa/Gandhi, Dalai Lama, etc for being so forgiving, but I'm going to assume you would at least dislike Bob for that,
It's a similar thing for the high table, they might not be best friends, but they are the High Table, an affront to one is an affront to all, so some revenge might be in order
Self Preservation
Come down hard as hell, and no one will repeat the same mistake (in theory)
If you punish everyone that helped Jon kill Santonio, literally everyone... then next time John needs help, you know full well that helping him will cost you your life.
Seems over the top, but think about it, then the next person might be another member of the high table...
And if one person (even if it is the infamous John wick) ignores the high table, then what's to stop others ignoring them as well, soon their entire power balance starts to become unhinged. It's better to show that you are not to be messed with in any way.