Maybe his petty beef with his fellow rich white dude overrides his transphobia?

Simpler than that - Elon doesn't believe he's transphobic, and in his mind pointing at "real" transphobes proves it.

As much as I wouldn't be surprised that Altman is a piece of shit, releasing an "open letter" by DMing it to Musk is just nonsense. 100% chance that Musk thinks he's really smart for making this, and no one will be able to see through his deception.