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I think the notion of this archetype is flawed to begin with.
Snow White is a fairy tail which I will mention the importance of that in a moment but even ignoring this, a new wife treating a non related child like that is nothing unexpected and happens the other way around as well. Lions will kill the offspring of a new pride it takes over because they are not related to him, I think something like this happens in Lion King but I don't remember that movie much. But of course, that's also the plot of Hamlet, kind of. So I don't think gender relates to it at all nor motherhood nor fatherhood.
Anyway, the reason Snow White being a fairytail is important is because fairytails are basically self insert fantasies for peasants children and the like.
The motives of the stepmother of Snow White or Cinderella don't really matter in this and are not the driving factor behind the story, the driving factor is the idea that a normal girl is actually a princess and the most beautiful in the world and that the only reason she is in her situations is because the somebody else is evil and force her away. It's fairly common in even today's media, the protagonist is often raised modestly but is actually somehow royal or special in another way all along they just did not know it because of reasons.
Starwars is an example of it and Starwars also has a parental antagonist though in this case he actually is the parent. Naruto is similar but a case where the parents are not antagonists, in his case the parents are good people but died when he was a baby rather than that a parent was bad and force him out, but you kind of have to pick one of these for such a story as if one's parents are good and still alive why would they kick you out as a child?