You're right, I think, to see (Cartesian) dualism in the kind of religious nonsense of one kind of trans ideology. Separable souls etc.
Do beware of oversimplifying, though. Two things:
--1. Not every religious ideology requires separable souls. Not even every Christian ideology. For example Thomist (as in Thomas-Aquinas-style) Christianity, is based more on Aristotle than the (neo-)Platonists (and Cartesians).
These latter see a separable soul as required for eternal life, whereas the Aristotelian soul, as the form (roughly-speaking, structure) of the body, is inseparable therefrom. (Hence, for example, 'The Resurrection of The Body' as an article of the (Thomist) Christian creed, necessary for eternal life if the soul is Aristotelian rather than Platonist/Cartesian.)
--2. Not every present-day trans ideology has the clarity of belief in (gender identities or) separable souls. The Judith Butler queer theory crowd are not Cartesians or dualists at all. They're not really anything in that line other than purveyors of nonsense. (And, yes, take it from me, it is nonsense ... not even, as they try to make out (JB herself a prime exemplar), clever nonsense: it's just plain ordinary stupid nonsense.)
(If you want a diagnosis, here's a start. To take the lack of transcendental signified as destroying signification and hence meaning is to mistake what should be a modus tollens for a foolish (and clearly invalid in its self-stultification) modus ponens. As should be obvious, it's not possible to make sense of denying sense in that way, any more than it could be true that nothing is true.)
It's interesting the two wings of trans ideology - gender-identity Cartesianism vs post-structuralist relativism - are so wholly inconsistent one with another. (Of course the ideologues of both stripes try to keep that quiet - sometimes consciously, we cannot but think.)
Either way, it's just plain wrong to allow such ideologies to interfere with childhood, whatever grownups get up to. We should, indeed, have learned that lesson from history, as you rightly say, @BigBadaBoom.