>>594171
This is, at best, analogous to when abortion advocates bring up rare cases when abortion might be licit. Even if we agree that these mutations put people outside the gender binary, so what? Transgender individuals aren't physically deformed. They're suffering from a delusion. It's not remotely the same thing.
It may even be completely missing the point of gender itself to ask whether intersex people have a different gender than male or female. If we consider gender to be different than sex (that is, biological sex as determined by the chromosomes), I can still only see male and female as real options, since the idea of gender as a social construct is still essentially linked to men and women.
Male attributes and concepts are defined as being necessarily or predominantly exemplified in men, and are almost always this way because of men's psychology or biology. Strength and soldiery are seen as masculine because men are naturally stronger and more inclined to use their strength than women, for example. Female concepts are also ultimately derived from the tendencies of women, naturally.
These tendencies of men and women, in turn, are the result of their natural roles in reproduction and child-rearing. That is to say, the male and female sexes are designed for different things. Yet, intersex people are not intersex by design. Children born with mermaid syndrome don't have a new, different type of legs, they have malformed legs. We can say this because we know what legs are supposed to be and do. In the same way, we know what sex is and what it's for. People who are intersex are malformed, and this is tragic, but it doesn't change the essence of what sex is any more than those children with mermaid syndrome change what legs are. And, since gender is defined by sex (albeit indirectly) even if it is "just a social construct", these people who are intersex don't change our understanding of gender, either. If you insist on calling them something other than what they appear to be phenotypically, as >>594176 said, then call them genderless, or neuter, just don't go pretending that this opens the door for any more genders. It doesn't provide precedent for people deciding their own gender, and that's what is being pushed for.