The problem is that "you do you" is an ineffective counter when the other side has decided to actively exterminate a minority group. "You do you" is fine in normal times, when there isn't an actively malevolent political movement bent on the destruction of a minority group.
This conflict is entirely at the feet of right wingers. Trans people have never been well understood or popular. But up until 2016 or so, we were mostly an afterthought. And honestly, that's fine. What the trans community really wants more than anything is to just be left the hell alone. But Republicans lost the fight on gay rights, and they needed another out group to target. So they moved on to trans people.
The conversation mostly works like this;
Conservatives: trans people are demons and we should exterminate them like animals
Liberals: umm, maybe that's not a good idea. How about we just let everyone live the way they want and not bother them?
Conservatives: why do liberals care so much about trans people??? Why do they never stop talking about trans people?!
Conservatives like to say liberals are obsessed with gender politics, but that focus is ENTIRELY THE FAULT OF CONSERVATIVES. And liberals don't have some general like of trans people. It's simply part of core liberal philosophy that you don't sit idly by while minority groups are attacked.
But again, if you actually want to stand up for someone's rights, you need to actually be able to rhetorically defend them. Consider this:
Conservative: TRANS PEOPLE ARE MUTILATING CHILDREN'S GENITALS
Liberal: I think everyone should live and let live. Let's just have tolerance.
Do you see how weak, ineffective, and utterly useless that is? When someone spouts a bigoted or racist line against a minority group, you can't just sit back, say "I accept all viewpoints," and do nothing. If you actually care about protect people's rights, you need to be able to actually defend them.
The problem with milquetoast centrist "live and let live" is that it's very, very easy to paint extremely damaging revocations of civil rights as simple "common sense" policies. For example, I described why it's a really, really bad idea to force trans people to use the restroom that corresponds to their birth sex. But a Republicans will say, "I don't oppose trans people, I just think we need some common sense rules to protect everyone." And if Democrat isn't actually willing to protect the rights of trans people, they'll end up going along with it as it seems neutral on its face.
Or, for another example. Consider "separate but equal." If you didn't know anything about Jim Crow and how utterly laughable the idea of separate but equal was, it seems fine on its face. And if opponents to segregation just took a "you do you" philosophy, they never would have stood up against Jim Crow. They would have just said, "ok, black people. You go do your thing, separate but equal, but I don't want to have to listen to all this identity politics. I'm sick of this woke shit."
I figured that was implied. :D