AP Stylebook.
Maybe I'm being too sensitive in this case, but I've always used the term "the President" or some such for followup references, and also personal pronouns, if needed.
I see so much routine disrespect for the President in the Media that I'm automatically suspect of it.
I guess I disagree with the AP Stylebook, and would be interested to see a comparative analysis of the AP's print treatment of President Trump—or other Republican Presidents—versus President Obama.
When I was in he Scribbling Profession, the Stylebook was our bible.
There was a time, pehaps decades ago, when the AP was the gold standard of news reporting.
Likewise, CBS News before the Cronkite era...