Setting for the SRPG that will only ever exist in my brain.

>What kind of setting is this?
Fire Emblem-ish fantasy with lots of monstergirls and such, who are incidentally responsible for the yuri-normativity.
Long story short: in the distant past, a brave heroine went to fight a powerful dragoness. They were evenly matched, and the fighting broke down and went wrong (went sexual), and something about their actions resonated with all the magic lying around from the heroine's broken equipment and the dragon's inherent magic and then boom. Suddenly there's monstergirls everywhere in addition to the existing humans/elves/dwarves/etc, but they're all-female and can reproduce with women, and they end up outbreeding the old races so that most people are women and like women.
Also, the crater where the "plap plap get pregnant get pregnant" happened became a natural landmark, though not everyone understands what exactly it is.
>Are men still around?
Yes, but only because I need men to still exist in significant enough numbers to justify that one of my characters is disguising herself as one.
>If men are around, [gender equality]?
Depends on the location. A few places are still dominated by the old races (that have men) and don't like the idea of being supplanted, so women have it worse there, but there are also places with monstergirl coexistence/dominance.
>How did lesbianism become normalized/institutionalized? What happens if a girl identifies as straight?
It was mainly a consequence of monstergirls coming into existence. They were initially attracted to women almost exclusively, and enough interbreeding skewed the tables over time so that everyone's more likely than not to like girls.
Being an entirely straight girl is basically unheard-of by the time the story starts, but she'd probably just be considered an oddball or a wet blanket more than anything.