Sure, different people will have different strengths and weaknesses. But that's different than "hard-wired." You may have some natural talent or predisposition, or you may have some particular disability or difficulty with something. But most of those can be melded and shaped by your environment, your culture, your experiences, your hormones, practice and learning, your desires, and the like.
I've known several people who have transitioned between genders. Were they "hard-wired" the way you claim they are? One of them, who transitioned to being a man, took testosterone as part of the transition (and presumably still does). He reports that the testosterone was significant in changing some of his behaviors to being more masculine; when upset, he has a harder time crying than he did before. Now, is that what you would call "hard-wired"?
I don't pretend to know whether you are born gay, or if it's something environmental during your childhood, or whether it really is more flexible than some people like to admit. Surely there is a predisposition to be attracted to the opposite sex; but that doesn't meet the criteria I would use for "hard-wired."
"Hard-wired" says that something is absolute; immutable. It cannot be changed. There is a binary; you are either this way, or you are that way. And that's just not how people work; at least, behaviorally, for the vast majority of behaviors. Really, there are multitudes of different axes on which people's behavior differs; and while their sex might influence their behavior a bit, the results tend to be overlapping bell curves with slightly different averages, not two entirely different sets of behaviors.
The whole "women do this, men do that" or "hard wired" type of reasoning is an over-simplification, which is amplified culturally.
(sorry for the late followup, I didn't see this comment until just now)