Speaking from my perspective both as a gay BattleTech player and one who in particular favors the Clans... beyond some edge cases (I'm thinking the RasDom and the Scorpion Empire, which have had to make some adjustments as they've begun sharing power with their non-Clan populations), I don't see the Clans tolerating divergent gender identities, or even acknowledging them in the first place. In fact, the Clans seem like
exactly the type of society that would be conservative and absolutist when it comes to sex/gender.
The Clans are all about conformity and have a pretty solid grasp on genetic sciences, and I'd think that if they haven't already corrected things like gender dysphoria with actual treatment of the underlying condition (as opposed to what is done in the real world, which is to alleviate the symptoms through social and sometimes medical transition), they'd just flush what they'd see as "bad genes" down the drain. After all, why would the waste-not-want-not Clans go through the expense/resource expenditure of transitioning someone's gender when they can just sterilize or even euthanize them and replace them with someone that isn't a resource drain? That seems to be antithetical to the Clan mindset.
And speaking again as a gay BattleTech player, I'm A-OK with all of this, because it's all fiction and the Clans have always revolved around this kind of violent conformity; it's baked into the very foundation of what the Clans were formed to be. The Clans are defined by a lot of things, and one of those things is their intolerance for that which is different, especially where genetics are involved. We've seen them stamp out entire sibkos for a lot less... hell, we've seen sibkos cull
themselves to weed out what they perceive as weakness, and as grim as it is to say, I just can't see the Clans not viewing something like gender dysphoria as a weakness, most especially the warrior caste.
snip
Literally none of this is accurate or cited anywhere in the source material. We've seen absolutely no evidence that Clan medical technology is "press a button and wait", either. Even their ability to replace/regrow severed limbs, one of their most advanced medical techniques, takes months of downtime, with some warriors opting for prosthetics just to avoid that downtime.
The Clans do have very advanced medical technology but it differs greatly from Canopian methods because Clan medical technology revolves around
necessity (i.e., surviving on their marginal worlds, keeping their warriors fit for duty, etc.), not elective medical procedures. In other words, the Clans' medical technology is top-notch but also very, very specialized, as opposed to the broader approach we see with the Canopians.
In fact, WoK points out that not only have the Clans focused their technological research on military efforts, but they've had very few advances in civilian technologies save as spin-offs of military research. The general level of Clan technology differs little from the Inner Sphere and even lags behind in some areas (such as entertainment), as they've technologically stagnated in most areas outside of weaponry, genetics, computing and materials chemistry.