I think it’s only important in matters of medical things whether a trans is a “real” woman or not. Some drugs won’t work on men, or have other issues, so it is important to know in that aspect. That should only apply in medical matters, though, and is pretty important.
A lot of trannies that aren’t passable are unfortunately going to catch a lot of shit from men. Sometimes, these situations might turn violent. I’ve had a couple trans friends I’ve taught how to defend themselves, and helped them get their carry permits so they can keep a compact pistol on them if they need to use it. I personally don’t like bigger cities, as I’ve had a couple of occasions where I almost had to shoot someone, so I try to avoid them.
I’d rather not have to hurt someone, but it is the only proper response to violence. Being a tall, slim, fairly feminine looking man, I’ve had my share of “macho” men try to use violence on me. Generally, staring down the wrong end of a Glock 19 changes their minds pretty fast. Fortunately, I’ve never had to actually fire on them, but they could see I was prepared to if they made more threatening actions.