The trouble with being "fed up with identity politics" as you put it in a comment, is that there's a whole group demonizing a portion of the population, and trying to erase that whole concept. It would be like during the civil rights movement saying that you are tired of all the racial politics, and expecting black people to just be satisfied with sitting in the back of the bus. It's ignoring the very real discrimination against a marginalized group.
I'm fed up with identity politics too, but it's more in the way that I'm sick of all the fear being spread about people. Since there's an active movement to suppress or even erase trans people, the right thing to do is actively oppose that movement, not just ignore it because I'm not a part of that group.
Essentially, a fight has already been started. By not taking sides, you are implicitly taking a position of not caring if this group is erased. And that is why this attitude is simplified down to "fuck gay and trans people"
I consider myself a true independent. I've never been in the Democrat party. I just think people deserve to be treated like people, not demonized simply because they live a different way. And I'm willing to stand up for that most basic of decency towards people.
You can say that's not the goal of the right, but it's still an active movement to that end. Personally I think it's just a tool the right is using to gain support by spreading fear about an issue that isn't fully understood. They directly spread propaganda suggesting that trans people are coming for your kids, when most trans people just want to live in the body they choose.
For example why is supporting gender-affirming surgery for any person a bad thing? In reality, nobody is pushing gender reassignment on people who don't want it. Regardless of who they are, their decision to have surgery doesn't harm you.
These are just people who have different emotional or psychological needs than you do, and even if you don't relate to it, that's okay for them to feel that way. Why shouldn't it be supported? What harm are they doing to you by being trans and having gender-affirming treatment of any kind? From that perspective, it's hard to see opposition as anything but being against who these people are as individuals. And that's precisely what transphobia is: opposing it for no reason other than that it's different from what you know.
We should fully support people being or doing what they want, until it becomes a danger for others. And we have seen that anti-trans attitudes have led to trans people being harmed or sometimes killed just because they are trans.