I think that is why, historically, most people conform to the current stereotype in public, and then only reveal themselves to close friends and their significant other. (And, again, I am not just talking about trans people here. Everyone experiences this to some degree or another.) The backlash for not conforming can be devastating because you have a small minority that will attack you for not conforming to their ideals.
Most people just want to be left alone to live how they want to live. So they keep their heads down and keep their private lives private. The trans community is experiencing what happens when you don't keep your head down. A certain segment of society will attack to try to keep people in line.
We saw this when gays & lesbians started coming out en masse. We saw this during the civil rights movement, when people of all colors stood up and said racism is not okay. We saw this during the 70's with the hippies and the free love movement. And we are seeing this with the trans community now.
Most people frame this as an "us versus them" situation, and on a personal level, it is. But when it is framed in principles, such as the freedom to pursue happiness and your right to privacy, most people can agree on that, and you have more allies fighting for freedom, even if they don't have the same life as you do. It makes it easier to fight the people who want to force you to live your personal life according to their rules when you have multiple diverse groups demanding freedom and privacy.
Plus, as we can see, divide and conquer works. If they get everyone divided up in their small little groups, each group is weaker and they waste energy bickering amongst themselves. But the reality is, most people want the same things: freedom to pursue happiness, the right to privacy, and to be free of harassment. Diverse groups coming together is the only way to push back those who want to control your private life, whatever that may be.