Actually, it is not hate that vets have for Kerry. It is betrayal and that he is not part of the band of brothers, but a wannabe.
The closest analogy I can think of is a person on a sport's team going their own way and, when off the court, saying that no one supports him, he is right, plays great, and the rest of the team plays poorly.
A contempt develops for that person by the rest of the team. He has betrayed them, but he is "part of the team". It is like the betrayal of a family member. The hurt is deep. But you keep your mouth shut, since you are on a team.
For a sport's team, when that person is removed, the team performs better because it is a team again. They will not bad mouth the player, since he was part of the old team. But if he starts mouthing off, they will comment and do so with energy- stating the truth, that he was not a team player and hyped his stats. He betrayed the team and them.
It is not hate. It goes deeper and there is a sadness to it.
Maybe we should start calling him John "Keyshawn" Kerry? "just give me the damn country" could be his motto.