If anything, the word "género" has historically only ever been used in the grammatical sense, while the word "sexo" applies to living things, including humans.

If anything, the word "género" has historically only ever been used in the grammatical sense, while the word "sexo" applies to living things, including humans. I would be very surprised to find references to the "género" of a person in any sources before the 20th century. It's not even that the words were synonyms; earlier speakers would have thought of referring to the "género" of a person as redundant and indistinguishable from the "sexo".