Does any of those mutations produce fertile individuals, with both reproductive organs fully functional though? I don't know enough to answer, but I believe that's what the parent is asking.
What I'm saying is, from a biological perspective, isn't sex determined by the gametes (which as far as I known, are two), regardless of vestigial organs, number of chromosomes, etc.? I think that's what caused the confusion on the parent about existing more than one sex (reproductive role); of course, by that measure, infertility is undetermined as it plays no role in reproduction.
Totally agree with you. At least in humans, there are two very clearly defined reproductive roles. Test tubes and surgical procedures can interfere a bit, but you can't be "mostly" a gamete donor or "only somewhat" of a gamete receptor.
Some inter-sexed people are fertile, but I don't think that's relevant to this discussion unless you also declare infertile cis-gendered people to be an invalid gender.
Biological sex is very complex but can appear simple with limited information because (1) many of the features are not superficially evident in gross anatomy, and (2) the majority of the time, most of the features line up in one of two main ways, making it seem like a simple binary thing.
And, in fact, there's research showing connections between transgender identity (where socially constructed gender -- usually based on the more obvious indicia of biological sex -- doesn't line up with gender identity) and instances where the various indicia of biological sex aren't aligned in the usual way. Its not, as I understand, apparently the only factor in transgender identity, but it seems to be a significant correlate.
The idea that gender ought to be simple seems largely supported by the illusion that sex is simple.
There's definitely a whole rabbit hole this way - lot of gender theory and stuff. If you're really curious, check it out, there are some interesting arguments (though few satisfying conclusions).