I just don't get it. I really don't. Why anyone should care about someone else's gender identity is a total mystery to me. Other than maybe to use to appropriate pronoun.
I'm a (as I like to say) boringly normal heterosexual. I was born with a female body, and am happily ensconced in that same body many decades later. On one hand, I don't quite get being transgender simply because that is not part of my personal experience. But I think I get that it would be a profound aspect of a person's life to feel that the body you were born with doesn't feel right.
In recent months I've been in situations where I think the person I'm talking to or being waited on or seeing interact with someone else is transgender. I'm always a bit bemused. I'm slightly tempted to ask a question or two, but never do. I simply accept the person as they present themselves to me. If they seem to be female, I take them as a female. If they seem to be a male, likewise. If someone gently corrects me about what pronoun to use, I accept that.
Several years ago in a shoe store I had a wonderful conversation with a young person who seemed to be male, but we were discussing high heels. It was a total delight.
What I most appreciate, even from my boringly "normal" heterosexual perspective, is the wonderful variety I now get to participate in, if vicariously. I recently read a collection of stories by a science fiction writer I know slightly. Some of the stories had women who had wives, and what struck me the most is how recent it is that such stories could be published. The author is a woman who, by her own casual reference to her wife, made me understand that if you're a woman and you're married, you're a wife. If you're a man and you're married, you're a husband. I'm only sorry it took me so long to understand this.