Well, I think hormone washes rather fail Occams razor, tbh. What is the most simple explanation for males or females in our culture feeling a sense of disconnect with their bodies which may relate to their preferences for certain activities and personality traits which the society around them has coded for the opposite sex? Is it the society around them coding these things erroneously, or is it a mysterious, unproven theory about hormone washes in the womb?
This seems how a lot of people interpret this idea, which you are right, doesn't seem to make much sense.
I think to some extent it's not actually the idea. It's more that culture encodes certain things as relating to male or female. Some may represent some real, though not absolute, connection, maternal behaviour say. While others have a random quality, like a certain colour or speech patterns, whatever.
I think the real idea is that for some reason, because the individual is somehow "identifying" (and I use quotes because I am not sure it's really the right word here) or maybe say associating? their body with the other sex, they are also picking up or are being sensitised to the encoding related to that sex.
Or what I think might be more likely or at least also occurs, because they feel alienated from their own body, particularly the sexed element, they pick up on the encoding related to the opposite sex.
As for why people might feel that alienation or affinity in their self-image, I don't think there is really evidence of the hormone wash business, but I do think there was some research at one point where that was being discussed. So it's not necessarily that people are pulling it out of thin air. I think it's more likely that it's related to other identity disorders but then some people think there could be biological markers for some of those as well.
But I think we are all pretty attuned to the encoding, we pick it up without even being aware that we are. That doesn't mean we are bound to follow it, other personal feelings can come into it, sometimes the coding itself is not so clear cut, and sometimes people deliberately subvert it for effect.