Munchausen by Internet

Great term

I don't know how to push back on this, especially in the current social climate.

Maybe try getting in ahead of it with non controversial teachings. Like, explicitly teach him that boys and girls can both like all toys and do all things. Maybe your husband can demonstrate that by playing dolls with him or baking with the kids or something and just teach him that anyone can play with and do whatever they like. If he comes over wearing a dress, point out that you're wearing pants, and not long ago women weren't allowed to wear them but now everyone can wear whatever they like isn't that great? Have a spare outfit of comfy clothes for him if he wants to change so he can play more comfortably. Teach him the difference between boys and girls, men and women, is physical. Boys have a penis, girls have a vagina. Teach him that only boys can be dads and only girls can be mums, but dads and moms can do all the same things (except dads can't be pregnant or breastfeed).

Hopefully if you get in early enough with enough clarity he won't be easily swept along. The push back will have to come from the kid himself in the current climate. You will just have to support him in being who he really is; a perfectly normal boy who likes and does all kinds of things.

Take photos of the dresses though, and record conversations with the kid and the mother. Hopefully you'll never need them as evidence and they can be just for him when he's older (and talking to a therapist about his mother's issues).