As I'm an SO, my advice on this is not from the perspective of the girl, but from the man. Feel free to discard what isn't good from it (even if that is all of it).
I think it depends on the type of relationship. I can talk about mine. My wife and I could be classified as "middle aged" when we met. We were each other's first serious relationship. Neither of us did the dating scene, neither of us wanted a quick fling. We met at an event where we both shared a common interest. I saw this very interesting person, and she likewise felt similarly about me. So we arranged for a lunch after the event together. We started corresponding and talking to each other, as friends.
Over a few weeks, it was clear to both of us that we were attracted to each other. She told me about things she felt I needed to know, and I did the same. This included a brief, non-detailed, explanation that she wasn't always seen as who she really was, but is now. It was matter-of-fact and done confidently. I won't say I was terribly surprised, nor will I say I ever considered dating anyone who didn't always have the right letter on her birth certificate. But there was a real attraction there.
In addition, at this point, she knew enough about me to know how I respond to diversity. I was glad she told me something she had no reason or need to tell me, but which is obviously something few would want to feel that they need to tell another person. I felt it showed tremendous trust in who I am and how I would respond. Since then, this trust has deepened our relationship - she can talk to me about her struggles, and I'm glad I can be a help to her when she's having a hard time in the world (just as I'm glad she can and does help me when I go through my own issues). I feel that there would be a depth missing from our relationship without it - I might not know it, if she didn't tell me, but I'm glad she was willing to share. Over time, we've both shared more about our past. I know there is nothing I can tell her about my past which would change how she sees me, even the things I am not proud of. Likewise, I believe she feels the same with me.
That said, it isn't my place to tell her or expect her to tell me anything she doesn't choose to. That's part of my trust and respect for her - I trust my wife 100%. If she doesn't tell me something, that's fine, I don't need to know. I would be shocked if there was much she wouldn't be willing to tell me, but at the same time that comes from trust and respect, and cannot be demanded.
I would say for marriage and adoption in the USA, it's a good idea legally for the spouse to know. It's also a good idea to remember that not all jurisdictions respect SRS or even changed birth certificates for purposes of marriage (so don't live or marry there if it would not be respected!). That's something as a spouse that is important to me too, because I do not want to have our marriage placed at risk either. I want to know my spouse will have no problem, for instance, claiming a life insurance policy if I die - even if the insurer doesn't want to pay up.
So...long post to say: you need to make your own decision, and you very well may do things differently - particularly if you aren't looking for a spouse! I would say in closing to dump any guy that "needs" to know and to dump any guy that wouldn't be able to handle it. You deserve what everyone does: a partner who loves and respects you.