The main thing that's being thrown around is that all trans women are sexual predators, just like how all homosexual men were in the media in the 70s. now, like then, only half the people involved actually matter, because trans men/lesbians screw up the debate.

one thing i heard a while ago that resonated with me is that the "natural order" people seem to believe in "rank" men higher than women. it's the classical "women are supposed to be meek and stay at home" bullshit. so, in a world where gender is sex, is fixed at birth, and gender roles are also fixed, trans women (or, to use "their" vernacular, men choosing to present as women) are intentionally devaluing themselves. if you are indoctrinated into the value belief, this action is completely illogical and unnatural.

there are two ways out of that philosophical dilemma: either you take a good look at yourself and reassess your own values, or you conclude that these people must have some nefarious purpose to their actions. they must all be molesters, or pederasts, or both, and they're using their presentation as a disguise to get close to weaker people in order to take advantage of them. again, the existence of trans men and lesbians completely invalidate this, so they are ignored.

the fact that, as the "weaker" sex, women are constantly preyed upon anyway, and trans women more so than average, just doesn't register, because in this world trans women are "men" and therefore can't be preyed upon. the fact that it takes several years to go through a full transition and get a gender recognition certificate is entirely irrelevant because these people just dress up and then rape women (you know, unlike men).

the entire argument falls apart as soon as you think about it for more than five seconds, but it fits very well with the religious outrage that pops up ever so often.