The carnist here attempts to claim that any insult a vegan uses constitutes an ad hominem in their position, which invalidates the vegan argument because it is a fallacy
An ad hominem is very specifically when the conclusion of the argument is derived from an attack on the person, not the other way around. An example might help: one ad hominem is if a vegan responded to a list of criticism of carnism with "You're just arguing for carnism because you're a lazy, self-righteous douche". In this case, that would be refusing to attack the actual arguments being put forward, and instead just attacking the person instead, as a means of discrediting their belief in carnism. You're then hoping for "No, I'm not lazy, I have a job, and how am I a self-righteous douche?" "Oh well let me tell you how..." and now you're discussing the motives for your position than the arguments for it.
What is not an ad hominem is "plants don't feel pain because they don't have a central nervous system, you idiot!". In this case, you're not intending to discuss the other person's motives, you're adding an insult to the end of an otherwise reasoned position. The reason to not accept that plants feel pain is the lack of a nervous system not that the carnist is an idiot.
In the first case, the attack on the person is supporting the conclusion; in the second, it is not. That's the key difference.
For instance, you may be on a news segment with only 3 minutes to explain a massive position. In this case, sometimes shortcuts are required. It's easier to say in 500 milliseconds, "dairy is murder," than to draw up a fully qualified thesis on the position given the time constraints. Or if carnists lose patience and are ready to walk away from an argument, then such things tools might be leveraged to force re-engagement. Real life isn't as clear as a sequence of arguments written in symbolic logic. Sometimes you might win the argument in symbolic logic terms, but your opponent just says "f* off" and walks away. Did you really "win"? Fallacies are tools that live in a squeaky clean world, but sometimes things are messy.
I don't know; good luck! Go forth with point 1 and use your own judgment. Just remember: is the argument being made on the basis of your character rather than a perky insult that's thrown on the side?