Are you sure? That’s almost the opposite of what I heard, which was that “gender” being used to refer to -inity arose as a euphemism to avoid using the word “sex”, because the word “sex” came to be more associated with specifically “sex-acts” (and that prior to it being used as a euphemism in this way, it essentially meant something like kind/type/sort), and only after “gender” began being used as a euphemism in this way, did people begin using it to distinguish between “gender roles” and “sexes”.

Except there's no mandate that "a male" and "a female" are of different noun classes, nor are the nouns for man/woman abnormally privileged in most cases. I know Dutch has fused masculine/feminine nouns into a "common" gender, leaving the language with effectively only the common and neuter genders. If I remember correctly, a similar thing has happened in Swedish and Danish. Some languages have various concepts of animacy driving the system. Some languages have shitloads of noun classes.

You can adjust your language depending on the biological gender of who you're addressing in English, but English doesn't have grammatical gender in any meaningful way. The concepts are largely orthogonal.

Calling it gender really is just a bad, misleading name in the grand scheme of things.

Are you talking about direct object pronouns? At least in the case of Spanish, lo/la is the pronoun for a masculine or feminine noun. It would obviously follow that it's the pronoun for a man and woman, respectively, the same way they would be the pronoun for any other masculine or feminine noun. I don't see how addressing men and women (as a noun) the same as you would any other noun in the language (save some irregularities) means that the cart is pulling the horse.