Hermaphrodites majority of the time cannot have children, so they're pretty much free to do whatever.
as long as they are married, but should they have male or female partners ? or only another hermaphrodite partner ?
I mean if you ask me none of this shit matters, but from the POV of those born that way who are concerned over it they tend to have more of a tilt towards one gender than the other, which they take into account as if it were their gender most of the time. It ends up being more about how they identify themselves, since at that point if they are concerning themselves with the binary as a member of neither what else can they really do?
They could seek out another hermaphrodite I guess, but I never see them talking about that being the solution.
https://www.gotquestions.org/hermaphrodites.html
I found this article interesting