It's not really a thing in ASL because it doesn't have to be. ASL has spatial pronouns rather than gendered (as in, the first time you refer to someone in a given conversation, you establish that a particular direction or area of your signing space is for referring to them). Sidesteps the whole pronoun issue entirely.

The more difficult thing is how gendered signs work. In ASL, feminine signs (woman, mother, girl, etc) are done at the chin and masculine signs (man, father, boy, etc) are done at the forehead, and there was a bit of confusion for a while for how you would even do gender-neutral versions of those signs- even "parent" was just signing mother and then signing father. But recently, people have settled on doing gender-neutral signs at the cheek (so, e.g. the gender-neutral parent is done by doing the same motion as in the gendered one, but going from the cheek to near the ear, rather than from the chin to the forehead)