So, Anglo cultures pushed women’s-rights, whereas Latin cultures … won’t, don’t, drag their heels, etc…

That’s mostly bullshit imo.

Grammar itself doesn’t necessarily hold back progress with gender identities and equality.
Languages evolve.
French can have gender neutral pronouns, which can make sense for referring to people of various gender identities.
Meanwhile, a gender neutral “table” is a bit moot. While a table is a feminine noun, such an object has no identity, its “gender” has nothing with social constructs, with gender roles or identities, not with women in general. A noun isn’t feminine or masculine because of its characteristics, but because of its phonetics and in some cases, plain old habit.
Synonyms can have different grammatical genders.

I’m quite certain that women are better off living in France or in French Canada than most places in the anglo US, not that it’s a high bar on the subject of women rights.