What is "traditional" code for regressive social attitudes - sexism, homophobia, and a host of other terrible ideas of suppressing rights and calls of mental illness. Lot's of regressive attitudes. My wife's nephew is Trans and is FAR from "mentally ill". I’d be willing to wager that his coworkers and neighbors don’t know what his genitals look like. The assault on trans people is not independent of homophobia, but instead just those same homophobes finding an easier target to focus on. Most people don't know any openly trans people so they don't get as much support, and it's easier to be angry about 'men dressed as women infiltrating our bathrooms' when you don't understand the actual issue or know of any people that it applies to.
We still have elderly people who grew up in a time where homosexuality was considered disgusting and sinful. You had people coming of age where, as time passes, homosexuality was seen as simply a different way of doing things. Obviously, some people will never change, whatever speed we go to denying people, in America, rights and human decency won't matter to them. Progress is often made simply by the old bigots dying off, and being replaced by younger people with different attitudes.
So challenging the status quo in a visible and assertive manner is important, so that young people realize that there are possibilities other than the terrible choices advocated by their hypocritical overbearing ultra conservative parents and their religious leaders. It's also important, of course, because if you're LGBT and living in some podunk town in the Bible Belt, it may stop you committing suicide if you can realize that the attitudes you see around you every day are not shared by the whole world. And it's time for such a person to either, fight or leave that bigoted regressive area of the country behind them.
No doubt there are some people out there who might now grudgingly accept gay rights, but "draw the line" at trans rights. But I'm highly skeptical that any of these people were ever enthusiastically supportive of gay rights - they had to be dragged reluctantly to where they are. What we're seeing now with Trumpism - people who never really wanted to give up any of their privilege and bigotry becoming empowered to celebrate their regressive attitudes openly. The movement for transgender rights is just the latest cultural "hook" for homophobes to hang their homophobia on. If the entire trans-rights movement went totally silent starting tomorrow, the homophobes would simply have to think up a different reason to foment outrage against gays.