I've even seen on Twitter spats with TRAs when a person explains "no I don't have a gender identity, I don't believe in gender" and the TRAs fire back "oh so you DO have a gender identity you are agender 😌😌😌"

I think they're drawing parallels that don't work when they say stuff like that. I remember a few years ago there were one or two exchanges I saw online between deeply repressed homophobic religious people who said stuff like "everyone's attracted to both sexes, you're just supposed to ignore your attraction to the same sex because it's sinful!!1!" and people who were countering that it's okay to be gay, where it was clear that the person was very much bisexual but very much in denial. (Obviously there are examples you can find too of gay people who are very religious and repressed, but they tend to not be so in denial in the same way, just self-hating)

So I think in those sorts of TRA exchanges, they're thinking of any opposition as bigotry and therefore when someone says that they don't have a "gender identity", they're seeing it as bigotry from someone who is so deep in denial that they don't realize not everyone is like them, even though they're right that most people don't have a gender identity

Either that or they can't handle opposition and need to fit people who don't fit their model into a box so their worldview makes sense