I don't know what kind of trigger warning would be needed for Disney discussions so I'm not commenting on that part.
The warning label for Disney could be that some of them are old and full of historical bias. And historical bias is the political correct way of saying that some works are full of racism and sexism.

It depends on the content you want to talk about. A general warning won't help to avoid trigger, stress or anxiety. Better to write your text, read over it, put it in spoilers and prepend content notes (CN) about the included points. These can be various traumatizing aspects and you can be really detailed as people have various stress symptoms. Food, harrassment, bullying, sexism, death - everything you talk about you can warn your readers with content notes.

Either way, should I place a trigger warning if making a post discussing Disney, or do I not actually have to?

How did we ever survive without trigger warnings?