Imagine if vegetarians started identifying non-vegetarians en masse with the label “Omnivores”. The first critique would likely be, “But it’s normal for humans to be omnivores; It’s the neutral state!”

I don't see the problem. Non-vegatarians/vegans are already called omnivores and it doesn't seem to be a problem. I wouldn't expect them to go out of their way to label themselves as such unless they were saying something like "I'm an omniVore" as a Vore joke. Carnists is the term that's used to be derogatory (although I think some weirdos who like to define themselves in opposition to vegans do call themselves that?). Likewise, "cissies" is a derogatory way to refer to the cis, but "cis" is just the neutral word used describe them. I wouldn't expect people to go out of their way to proclaim their cisness, but getting upset that the term exists and people use it is mostly just a bit.