If you're going to look at the genetic level, the presence of a Y chromosome is indicative of a male. There's no such thing as an XY female. There's also no XXX males - genetically, a person cannot be male without a Y chromosome.
Kleinfelter's is when a boy has an extra X (XXY). Girls with an extra X (XXX) have Trisomy X, or Triple X syndrome. Both of those are by definition genetic anomalies and are a separate issue from the LGBTQ conversation.
It has been shown by research that there's no single genetic connection with homosexual tendencies, but there are a number of different genetic markers that are appear to occur more frequently in that population. My understanding is that most of these relate to how various processes in the body are regulated, not to production of any particular hormones, and that the likelihood of any one gene or combination of them is a truly reliable predictor of whether an individual will have same-sex tendencies. Seems like certain combinations increase the odds, but it remains a roll of the dice.
One could argue that these genetic markers constitute a "disorder," and that they can be engineered and "fixed." They probably could be engineered, but I would argue that in most cases, these aren't mutations or anomalies, they're uncommon but apparently natural outcomes. The idea of "fixing" them at the genetic level opens another social can of worms.
In the end, I agree with several things that have been said: trans athletes should compete against those of their biological sex, not those they pick. We should not rewrite every publication to sanitize every reference to gender, race, or ethnicity, or pull down statues of everyone who's every said anything offensive to anyone. We should not burden 95% of our society to make 5% more comfortable. We should stop practices that are clearly discriminatory, but also recognize that there's no way to make everything 100% fair to everyone. We should find ways to help people that are struggling (mentally, financially, etc.), but also recognize that they have to earn it. We should punish people who break the law, but also acknowledge that there may be extenuating circumstances. For a lot of us, we should recognize that if you look at the root of an awful lot of our social issues - white collar crime, suicides, mass shootings, sex offenses, the list goes on - the people that are the problem aren't dark faces, kids, foreigners, etc. They're white men between 30-50.
We should recognize that everyone around us is dealing with their own sh*t, and odds are that a lot of them have a bigger pile than we do. It might be a good idea if, instead of complaining about the smell, we grab a shovel.