Of course it was legal - this has been litigated many times, which is how you end up with public servants (e.g. Police officers) being fired for being racist on "personal time".

You can't fire them for the speech - which is of course protected - but you can fire them because they can't possibly be qualified to hold their position while holding/espousing those views. Unless there's a specific state law protecting employees from off-duty conduct (Pennsylvania doesn't have one), employees can certainly be fired.

She specifically alleges that this comment about Muslims was not hers. I do not have any way to know if that's true or not--and I find the article's notion that she should know who did make an anonymous online comment incredibly thoughtless--but if that's true, your entire argument is wrongly premised.

I would think that she would want to prove that statement falsely attributed first in a defamation suit before going after the university.

The test above is correctly quoted, the only dispute is factual which none of us here has the evidence to resolve. She may be lying or telling the truth, but we can't make any grand pronouncements about whether the university was right or wrong on the basis of disputed factual claims that have yet to be resolved in court.

If she succeeds in proving that she didn't make the one comment about Muslims wasn't made by her, and thus she was defamed, then she would have to prove that the university fired her for that comment and only that comment. Seems unlikely to me.

If discussion here is anything to go by, that one comment is what everyone hates. I haven't seen even an allegation that the other comments were offensive in the same way yet. Even the article here makes it the centerpiece of their criticism.

And it's the one comment she says she didn't make.

I wonder if her lawyer has seen this story? Many of the comments here could be helpful in showing damages.

If it wasn't legal, why wouldn't she be suing on those grounds instead?