I would say, based mainly on talking to people myself rather than anything I have read, that there are a lot of people who seem to think that conservative religious people believe that there is some kind of gendered soul, separate from any kind of embodied element, and that there is some set of rules, like boys not playing with dollhouses, that the RCs believe has been set out by God, or the Church, or whatever.
In fact I would say that in my experience many of those people look at religious strictures in general in that way, as kind of arbitrary god-rules, like not wearing mixed fibers. Things people are meant to follow to be good but with no inherent importance or material cause.
Whereas in reality, I have never met anyone, including very conservative people, who thinks that there should be, or are, that kind of very strict rule around things, and they think that it is all pretty normal for girls to be tomboys or boys to want to play with dolls.
I know people who have these strict rules exist, but I don't know that they are typically actually very religious, or even really conservative. Like Susie Green seems to have been.
There have been quite a few times on these boards that people have argued that gender ideology comes out of a religious mind-body dualism.