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).
Case in point : https://www.youtube.com/watch?v=fpQmJ7UUNFQ >> Warning, this is not for the faint of heart. <<
I've worked in a slaughterhouse, doing the night shift cleaning up the mess before a new day begins, I know what's it's like. Overcrowded boxes full of chicken shitting themselves, getting hanged by their legs on a factory line before getting their throat sliced by a fast spinning blade. Not a pretty sight for sure and a sad way to go.
It's very unfortunate how the mass consumption of meat creates terrible living conditions for the various animals we breed for that purpose. But if we measure the scale of suffering, I think we're doing a bit better than nature.
And yes, by going vegan you do not contribute to that, I get it. I have huge amount of respect for people that live by their moral standards and stick to it. Yet this doesn't mean that the wilderness is some Disney fantasy and yes, for all intent and purpose, most animals out there in the wild are bound to have a gruesome end.
I'm not implying that we're doing animals a favour by sending them to a slaughterhouse, simply that this is the natural order of things. If you feel strongly about that and choose to not consume meat and such, great. As for me, despite what I've seen, there's nothing wrong with eating meat. The only thing I wish is a more humane breeding, and I'm happy to pay more for that.
I'm aware that it's slightly hypocritical because would there be an alien specie doing the same to us, I'd probably would have a different perspective on that. As it stands, I enjoy being an apex predator. May it last forever.
I think portion control would be a more effective approach. A little meat goes a long way. I think you'll get further convincing the public with a moderation message than a black and while moral argument.
A few ounces of meat/fish a day aren't going to cause any of those diseases and are packed with nutrients that a vegan diet has a very hard time providing at a similar cost, especially in poor countries. The Gates foundation isn't betting on chicken on a whim. I still think moderation is the way to go. If everyone cut their intake by 50% we'd have a healthier population, animal slaughter would be cut in half, and we wouldn't have to reinvent meat.
We probably could move away from meat, if everyone was well off (and took supplements). But that's not the case. And I never said 100s of millions were acceptable, merely that a 50% portion reduction is a LOT better than nothing, and probably a lot more than a morality strategy will achieve.