Yeah, to my ESL ears man/woman are nouns, not adjectives, and using them as adjectives comes off as childish.
That said, “female X” can also sound clumsy, if it’s implied that a bare X is male, e.g. “politician” and “female politician”, vs male and female politician. There was a twitter account calling itself a “male programmer” which took the piss out of that trope.
So, a mastodon user? :^)