I have to say no, I'm only ever going to date or be in a relationship with natural women.
It has nothing to do with being able or incapable of having children, it's a matter of my own personal tastes.
I consider transgendered, post-op ladies in the same light as dating a man, you may not feel like you're a man, but you weren't born with a womb, whether it functions or not is not important.
I'm not even bothered about having kids, if it happens when/if I meet a woman I want to share my life with, then I'll be the best dad I can be, but much like marriage I don't see it as essential to my life, more the sort of thing I would commit to if it was of the utmost importance to the girl I love.
If the girl I loved wanted kids, but we couldn't have them for whatever reason, then I'd happily adopt, but she'd be a natural woman.
If I found out that a "girl" I was dating or was in a relationship with was transgendered after we'd been intimate or even kissed then I'd feel betrayed, it's something very important that I feel I have a right to know about a person I'm seeing and honesty is very important too me.
I'd absolutely have to end things with that person if I started to spend time with them with a view to a romantic relationship and I found out they weren't a naturally born woman.