I...disagree. I think you would find that most of the left takes as an article of faith (or, at least, a very strongly held belief) that gender identity and presentation (which necessarily includes stereotype-conforming as well as nonconforming identities and presentations) are very strongly genetically determined and that extreme distress results when people attempt (or are compelled) to mask what is genetically-determined in this area, and that that is fundamental to the belief that nonconforming identities and presentations should be accepted.
> There's a lot of emotional investment for many in the idea that stereotypically gendered behaviors are entirely or almost entirely caused by culture/social pressure.
There's a lot of emotional investment in the idea that the concept that there is a single acceptable relationship between external genitalia, gender identity, and gender presentation is a social construct, as well as in the necessary corollary that the particular relationship chosen in any particular culture that imposes such a single acceptable relationship is also a social construct. But that's intimately tied to the idea that each of those three things, while they may have some non-genetic contribution, is fairly strongly genetically directed, and while there may be some correlation between the genetic determinants of each, there is considerable individual variation, as well.
For example, if stereotypical male/female attitudes and behaviors were found to have a substantial genetic component to them, I think a lot of socially progressive people would hate that. There's a lot of emotional investment for many in the idea that stereotypically gendered behaviors are entirely or almost entirely caused by culture/social pressure.