@Buttermilk,
It doesn't seem to me that if you would not date a transsexual woman because she was originally a man that you can honestly say that you accept her full transition to being a woman.
I think your trying to have your cake and eat it too, or just didn't express your thinking clearly enough.
As has already been noted, your idea
is discriminatory.
If you are willing to consider and treat the hypothetical transgendered woman as you would treat any other woman, but you will not date her because she is a transgender, than you are, quite clearly, discriminating based on her gender status, and not on a characteristic that would otherwise be a common reason for discrimination in deciding whether or not to date someone: physical appearance, age, personality etc. (the hypothetical laid out indicates your decision is based solely on her gender status and I'm assuming that is your intent)
Your friend is right in a literal sense, but it seems clear that she like many other liberals (whether or not feminist or LGBT) is of the belief that discrimination is automatically a negative thing. I suspect you may share her belief (at least to some extent) hence the offered defense "I accept (her) full transition to being a woman."
Again, clearly you don't or, all else being equal, you would date her.
I would hope that it goes without saying (but I can only hope) that you are not under any moral or ethical obligation to date a transgendered woman, even if she looks like Jessica Alba and has retained zero masculine characteristics. It appears your friend believes you have an intellectual or political obligation to do so (she probably thinks you also have a moral and ethical obligation as well but that's a given). You don't
What you seem to be asking is, "Is it wrong to deny that a transgendered woman is actually a woman; to believe that despite whatever operations and hormone treatments she has undergone or how she views herself, she is still biologically a man?"
I don't think so, and even if it were I don't see how you could possibly change such a fundamental perception. It's not a series of consciousness raising sessions is going to bridge that divide.
Personally I think the only "correct" behavior in this case is to treat the woman as you would treat any other woman for whom you felt no sexual attraction, and this would include your reaction to any romantic or sexual overtures. Probably safe to say that if an unattractive woman flirted with you or asked you out you wouldn't say something like "Are you kidding you ugly cow?" so you shouldn't respond to the transgendered woman with "Are you kidding? You're a goddamned man!"
The transgendered can reasonably only expect to be treated as the sex they believe themselves to be and in the same civil manner we all expect. They shouldn't expect people to change their hard-wiring.