As a cis-male, my opinion should not count for much in this as I don't have the experience of others.
But I'd suspect that having a body that matched your gender would increase a person's self-confidence and, thus, impact attraction in all the ways that self-confidence does for cis-women. Confident women - just like confident men - are more selective (not necessarily in a physical sense), among other things.
I'd also suspect that most people identify as female - whether cis- or not, pre- or post-op, etc, would probably not be attracted to someone who saw them as either male or as a third category. Most people aren't attracted to people who make them feel worse about themselves, and I suspect being treated as male or a third category would make most women feel worse about themselves. Of course I'm sure there are plenty of exceptions, and, once again, my opinions are not those of someone with first-hand experience, so I'm willing to be corrected by those with that experience.
