Well if you follow my argument about genetics, it should be possible to engineer arbitrary new genders, with enough generations of breeding, or gene manipulation.
Also not a very good argument. Evolution is a free-running, iterative, cobbled-together thing in a great many ways. Just ask the vast number of transposons in your genome. As long as one doesn't jump into the 2% of exons or 10% of introns you'll probably be fine. And if it does, even then it won't have any bearing on your heredity because they're so deeply entrenched in the genome that getting rid of them is actually impossible (and perhaps even harmful because they may be vital to maintaining the superstructure of your DNA).
In short, evolution does anything it can get away with. Evolution might not even regulate non-binary genders. And even if it does, there's no conclusive evidence that non-binary genders are significantly detrimental to reproductive fitness across actual history.
The amount of genes that differ between individuals is very small, due to natural selection. Only traits with little effect on reproduction will have high variance. Anything that affects reproduction suffers STRONG selection pressures. So they're just the sorts of traits which
shouldn't vary very much, in evolutionary terms.
both sexes interest in breeding with the other sex should be the #1 evolution pressure, you'd think. That's what it's all about actually. And the mother nurturing her young. Universal trait in all mother animals. No reason to think it's different with us. Sure, a "counter example" might be penguins, where the male watches the egg. But that's not really a good counter-example, because it's just another example of gender dimorphism in complex behavior related to reproduction that has arisen via evolution, and is pretty much universal to those species.
Also the traits we are talking about that differ, are also well within the range of behavior traits we see in non-humans, which vary by gender. Occam's razor comes into play here. Why say "it's too hard for evolution to do that" in our species, when it's clearly not too hard for evolution to make male and female chimps have similar behavior differences?
And your argument that non-binary genders have no connection to reproduction? It's a logical fallacy, for the main reason that what we label "inherent gender" are exactly those behavioral traits which increase the reproductive "fitness" of their associated biological sex, while being worse for the Darwinian "fitness" for the other sex, than some other option. If a trait had no particular reason to be associated with either gender, it would either die out (if it was less good than some rival gene) or become universal to both sexes (because it's beneficial to have for both genders), therefore it wouldn't be part of "gender" at all.
Actually, the argument that "any trait could be associated with either gender" is the clincher. Sure, I totally buy that. But look at chimps again. We see universal gender dimorphism in behavior. The non-binary theory should say that any chimp, by definition could get any behavior. But that's not what we see. Any behavior
could be associated with male or female, with equal probability. But the process of natural selection ensures that
that never happens.