You don’t have to read tea leaves: https://www.kff.org/other/press-release/poll-large-majoritie... (“In each case, large majorities across partisan lines, including more than 7 in 10 Republicans, think such discrimination against LGBTQ people should be illegal.”). That’s from 2020. Does it make sense that the majority of conservatives are upset about “the existence of transgender people” but somehow support making it illegal to discriminate against them?

The culture war came later, when liberals tried to use trans people to promote their own view—which you aptly characterized above—that people should be allowed to express themselves free from traditional social norms and roles. Liberals rushed to promote things like drag shows, which have nothing to do with trans people, and everything to do with voluntary self expression. As RuPaul (a cis man) put it: “Drag says 'I'm a shapeshifter, I do whatever the hell I want at any given time.’” That liberalism is what has “conservative parents riled up for a culture war,” when they mostly didn’t bat an eye at actual advances in trans rights.

Yeah unfortunately for conservatives, the annals of history are generally a story of culture evolving more rapidly than traditionalists are comfortable with. We happen to live in a country where the core Constitutional answer to that problem can best be summarized as: tough shit, get used to it. You can move to Saudi Arabia if you want to live in a traditionalist autocracy that will protect you from the horrors of drag brunch.