To be clear, there’s nothing wrong with using female as an adjective.

A female customer / politician / patient / etc is perfectly fine and normal.

The problem comes when you use it as a noun.

Think of calling someone “a gay”, “a black” or “a Chinese”.

You just don’t use adjectives-as-nouns to refer to people, apart from a very limited set of exceptions.

Instead you talk about a gay, black or Chinese person.

The same goes for ‘female’.

And since there’s already a word for ‘female person’ - ie. ‘woman’ - then going out of your way to avoid it makes you sound like a raging incel.