Probably by talking to centrists, I've come to a similar conclusion. Every single centrist I've talked to in person either refuses to use preferred pronouns, are outwardly disgusted by the idea of a trans woman, dont want them using their preferred bathroom, or are afraid of "trans indoctrination" in school (they dont want trans people mentioned or talked about in any class context). Idk, i know anecdotes arent strong evidence, but based on my experience, i don't think they pulled this conclusion from nowhere.