Some might consider that using them is a sign you agree with the concept of gender identity though. People should be free to use or not use preferred pronouns as they see fit.
This implies that as you reject the notion of gender identity that you would use your freedom to call a person he, regardless of their preferences, stated or otherwise, if you suspected them to be a biological male.
Presumably you'd also object to calling trans man "he".
You later caveat it by saying you would employ the pronoun "they", which seems odd, given your absolutist stance. "They" is either a tacit acceptance of gender ideology, or a safe word to employ if one is not sure of a person's sex. But what if you were sure?
There is an inconsistency here.