I'm stealing this line from someone else somewhere else: People's political views are primarily shaped by life experience. Today especially, life experience is shaped through media consumption.
Phrased that way, I think LGBT culture issues are of a piece with black politics and feminism. (No, not just because these issues are relatively united by the blue tribe and the culture war.) There are some ideas that, once you believe them, become self-reinforcing. If you believe that men are dangerous to women, you start finding evidence in your daily life everywhere. If you believe cops are racist against black people, your negative interaction with a cop transforms into your racist interaction with a cop. It becomes harder to tell when you are actually directly experiencing discrimination, versus when you are interpreting normal slights as discrimination. Especially today, when life experience is shaped mostly mostly media consumption.
We live in a sort of media hyperreality where things become real by being talked about. A few crimes against Asians, and we say there's a trend. Now, every new crime against Asians is evidence for the trend (fairly or not). Eventually, it becomes impossible to deny that there is a trend -- look at all the evidence! First we create the narrative, then the narrative creates us.
I had this similar experience with an aunt at my family. Here she is at a funeral complaining about how her family never accepted her because she's gay, and that's why she had to cut them out. What am I supposed to say? -- It's not true, she was never discriminated against, she's not even the only gay member of the family. Of course, in my family, this particular drama is much older than modern media consumption. I would guess this is a much older problem that is merely becoming more common today.
But I can't really argue someone out of a position they were never argued into in the first place. Personally, I've found the best tact is bland ignorance: "Really? I didn't know, that's too bad." Trying to argue against the narrative, I only end up playing into it or worse. ("Now you're discriminating against me, too?!") I listen politely, reminding myself that if I believed what my aunt believed, I would believe what she believed too. Then I change the subject.
For the same reason, when people grab onto an identity, it is usually a substitute for something else. There is some other problem in their lives they are trying to solve by aggressively conflating it with some identity. A lot of identities today especially are vague and squishy, all self-identities.