I don't think it's a cognitive dissonance thing, at least where I've seen that picture. I think it's an us/them thing. Specifically, the kind where one group gets the idea that another is out to get them. (That "militant vegetarian" you mention is someone I have heard about my whole life yet never met.) If they don't have a lot of vegetarian friends, you may be their first chance to have a conversation about it, and that's probably the only one they rehearsed.
It may not be as crystallized as other areas, yet, but I think this is also one more field for cultural proxy wars, as we all get drafted into us/them camps. Again, at the individual level, you might notice the person doing the attacking always thinks they're defending. Complicated big picture stuff at play.
Don't project onto people you clearly don't understand. Creating mental models of people you disagree with that involves making them stupid or living in dissonance does a disservice to yourself (by making you ignorant), to them (by you spreading your ignorance), and to wider political debates in general (it's very difficult to come to an understanding when people are incapable of understanding the other side).
I carry that cognitive dissonance (I know animals feel; I believe they have souls; and yet I continue to eat meat); the difference is that I (through tons of introspection) have made peace with my (very few) dissonances and therefore, calling me out on it (as someone did further up the comment chain here) will result simply in me acknowledging their observation (without any emotional/anger element).