The anti-trans social conservatives understand correctly that gender has both an external component (our reproductive organs) and an internal component (our psychological makeup), which are aligned or matched-up in a certain way in most people. What they are unable or unwilling to see is that exceptional cases may exist where the matching is different from most people. (Were this not the case, it would be the only phenomenon in all of nature that hasn't got a single exception or deviation.) They imagine that transgender people are "trying to destroy society".
Anti-trans feminists (or TERFs) make the opposite error, and deny any natural correlation between reproductive sex and innate gender identity. For them, all gender identity is "socially constructed" and the product of patriarchal stereotypes. From there, it is a short step to declaring all generalizations about men and women inherently oppressive and evil.
Of the two errors, the latter is more useful to socialists and radical leftists (who really ARE trying to destroy society) because it attacks the process of organizing our experience on the most fundamental level - it attacks reasoning itself. A botany book contains idealized diagrams of flowers, and an anatomy book contains idealized diagrams of people; no one imagines that these diagrams represent every case, or even exactly represent a single example, but they are useful tools for learning the overall properties of the thing under consideration.
It is not so difficult to say, "This is the general case, but execptions also exist. Each case is unique, and yet certain things are true of the overall population." And yet this is exactly what political correctness aims to do, with the intended and demonstrated result that the whole educational process grinds to a halt. And this is precisely what we've seen in ecucation for the past 50 years or more.