Why do you call him Tanner? His name is Byron.
— E.W. “Doc” Parris (@EWDocParris) June 8, 2021
"Doc" is upset that one of the first teachers speaking out against tranny nonsense was temporarily reinstated. (Loudon School Board and Tanner/Byron Cross reached a settlement a few months later, and of course Loudon ended up propelling social conservative Republicans into office, a story which continues to feel repercussions).
Doc thinks he's scored a point here though it's not immediately clear why. I've written about this topic before in a way superficially aligned with Doc's comment: Ellen Page is still Ellen Page and she will always be Ellen Page.
The "she" there isn't just an overly verbose qualifier (despite the fact the sentence can literally work without the word in there): it's a fundamental statement about who Ellen Page is. The issue isn't whether she could have said she wanted to go professionally by Elliot Page, the issue is that calling her Elliot is to participate in the fundamental lie that she's a man.
The Tanner/Byron schism isn't quite in the same league. After all, nom de plumes have been around for a while (check who wrote this blogpost, for example). Stage names are of course a similar thing. While calling Tanner Cross by the name Byron Cross isn't necessarily wrong (neither is referring to the voice actor who played the bad guy in The Simpsons Movie as Albert Einstein), it may be said to be unclear.
There could be said to be a spectrum, to borrow a hip phrase, with using the name a person chose rather than their real one. Abdullah Shah (who died this spring) occupies one spot on the "kinda wrong" side of the spectrum. Elliot Page is even further down the wrong side. On the other, there are stage names like Stefani Germanotta's or Calvin Brodeus' or Albert Einstein's. At the far end of this good side would be people who go by their middle name because their first was too similar to a living relative.
Tanner Cross can safely be said to be on the same right side of that ledger. Maybe we need to use a simple metric: if Twitter lets you use the person's old name, then it's not a big deal to use the new one.