I think that one thing I was doing without realising it , when I wrote this post, was thinking about the sort of arguments you see on reddit. (As opposed to debates in congress, for example, which I don't get much exposure to.)

I don't think it's uncommon to see redditors accuse a pro-lifer of just wanting to punish people for having sex, or to exert control over women's bodies.

I do think this is less of an issue with vegetarianism, but the vegetarianism debate seems to be less heated. I've seen people on facebook say that it's okay to be vegetarian/vegan but you shouldn't force that choice on your cats and dogs; but it came with the argument that cats and dogs can't be healthy without meat, which makes it not a great example. (It might be wrong for humans to eat meat, but not wrong for humans to feed meat to cats and dogs.)

I did a search for PETA, expecting to find people calling them fascists in some sense, but didn't find much. Vegetarians accusing non-vegetarians of being rakes seemed more common.