My wife tells me that using as an adjective is just as bad and that I should always say “woman”, e.g. a woman politician and never a female politician.

Using a noun as an adjective is just weird, honestly.

I think that a good rule of thumb is: would you say “male doctor” or “male politician”? If not, is the professional’s gender relevant? Probably not, in which case it sounds pejorative to include it.