Would I say "Trump only sees you as a cotton-picking n----r" to a black Trump supporter? Yeah, if the context was right (like it is in the example). Hard r and all. Because it's true - that is what Trump thinks, even if he's smart enough not to say it (often).
That's not the same as me calling them the n-word, I'm stating what someone else thinks.
Of course I wouldn't call a black person the n-word. Not because I'm afraid of the word itself, but because I genuinely don't believe in the image of black people that word was meant to create.
But Trump absolutely does. And it's ok to call a spade a spade. Important, even.
But the person replying isn't saying that Caitlyn ought to be referred to by her former name. In fact, they aren't actually using it to refer to her at all. They're merely mentioning that it exists, which is appropriate in some contexts.
If I were going over medical records with my doctor, she would be fine to ask if (deadname) was my name, because it's for a necessary purpose. That's different from using it to refer to me.
Also, if Caitlyn is offended by seeing that name, she's going to have an awfully rude awakening coming under the current administration. I think the time for subtlety is past on that front.