Does it have to be a protected trait? If someone (or several someones) decide they dislike me because, say, I'm ugly and they're just tired of seeing my face, and they start saying that I need to be fired, and putting ax icons next to my name, and going on Twitter to tell everyone how ugly I am and how it ruins their appetite for lunch when I walk into the breakroom, is that not a "hostile work environment" just because ugliness is not a legally protected trait?

If you did that kind of stuff at most places I've worked, you'd get fired for it, regardless of whether it fit the legal definition of "hostile work environment".

It may be a good idea to fire someone who participates in that behavior, but there isn’t a legal obligation to do so (IANAL).

If the behavior is because of your race and they aren’t fired, you can (successfully) sue your employer. That’s the difference.

In her letter, she asserts that behavior that fits the first scenario is illegal- it’s not.

Funny how a generic "toxic behaviour" is an accusation good enough against those with a different ideology, but when it's our ideology we go all legalistic.