Backed by thousands of years of precedent and a myriad of religious texts, reactionaries believe that gender is immutable and is established at birth. Furthermore, they believe that only heterosexual sex is “normal” and that any other kind is unnatural and an offense to God. State action is necessary to prevent society from being polluted by people who engage in unnatural behavior. Woke people, on the other hand, think gender and sex are fluid concepts and reject the concept of “normal” sex; in other words, everything is normal, and a society that imposes a single idea of normality on all of its citizens is oppressive and unjust.
As with race, there is plenty of middle ground between these ideas. You don’t have to accept the woke idea about sexual fluidity to oppose state action discriminating against trans people. I think that’s where most Americans stand today.