Gender' only exists in social contexts because it is predicated on how people perceive and attribute certain characteristics based on one's sex.
Yes
The problem is not one's sex - but one's feelings about it based on what one thinks is expected because of it.
I don't think that's quite right.
These feelings aren’t caused by what someone thinks is expected of their sex. Gender dysphoria isn’t about believing “boys should like football” or “girls should wear pink.”
It's a deep-seated, embodied sense that one’s body or sex category is wrong. The distress isn’t produced by stereotypes; it’s about the body/ sex itself.
A child may hate the colour pink, prefer football to netball, and have no interest whatsoever in conventionally feminine things. Yet every day they may still beg to wear a pink dress and play netball—not because they enjoy those things, but because doing so allows them to be recognised by others as the girl they feel themselves to be. The pink dress isn’t the cause of the dysphoria; it’s an attempt to alleviate it.
So yes we could eliminate the idea that certain colours or sports are for boys and girls (and we definitely should because gender stereotypes suck). But there’s no reason to think that eliminating those stereotypes would eliminate gender dysphoria, because those stereotypes weren’t what caused it in the first place.
There is, however, a more philosophically interesting argument. If sex categories themselves had absolutely no social meaning or consequence, perhaps gender dysphoria would disappear because there would be no meaningful category in which to feel misplaced. I can see the logic in that.
Even then, though, people would still have different bodies, and many people with gender dysphoria experience profound distress about those physical characteristics themselves. And in any case, the premise is entirely hypothetical. Sex categories exist because human beings are sexually dimorphic. Those biological differences have significant social consequences—for example, only some people become pregnant. It isn’t realistic to imagine a society that simply doesn’t notice or attach any significance to those differences.
So no, I don’t think it’s accurate to say that gender dysphoria can be “cured” by abolishing gender stereotypes. Those stereotypes may influence how dysphoria is expressed, but they are not generally understood to be its underlying cause