> clearly improve readability
Not necessarily. Some people object to singular they on grammatical grounds, in that it may confuse the reader who associates the pronoun with plural meaning only into thinking it refers to some previously unmentioned group. Infamously, Monica Cellio’s dismissal was more or less over this.
I happen to prefer singular they over he/she, but I acknowledge it’s not an obviously uncontroversial choice.
http://cmosshoptalk.com/2017/04/03/chicago-style-for-the-sin...
It's in the APA style guide (it's been there for a while now.) IMO that's even more pedantic than the "begs the question" battle which was lost some time ago.
I would saw we are all "non-binary". We fall somewhere on the spectrum of gender. Some men are "alpha-males", whilst others are more "camp" [0], etc. Also see "tom-boys". I find the whole non-binary thing to be unhelpful and meaningless.
[0] hopefully these aren't offensive terms.