Here is, from a purely heteronormative and fundamentalist (VERY fundamentalist) (yes I'm the only one now; all ideas start with one person) Christian POV, the benefits of knowing with 100% certainty who is a "woman" and who is a "man" and, of course, who are the "mutants" (hermaphrodites et al).
How?
EASY!!!
Enforced namespaces. No more "Pat"s or "Vivian"s or the like. At birth, you either choose a name from the male list or the female list based on the ruling of 3 farmers. Any disagreement means the first name on the birth certificate is, wait for it, "Mutant" or "Mutie" for short.
Yes, you may invent a new name at that point and it'll get added to the appropriate list. Yes, certainly, a person may change their name. They must first undress in front of 3 farmers.
So, a "man" knows by definition who he can date by checking the papers of any "woman" who presents said papers to him. Then, and only then, can he start the mating ritual.
Any questions so far? If not, I will now cover the details of said mating ritual.