so, is hate speech free speech?

yes.

but, all that means is that the government shouldn't be regulating speech, even if it's "hateful". that doesn't mean that the "hateful" speaker has a right to be heard. free speech also means that protestors have the right to drown out the "hateful" person, and prevent them from being heard, if they really insist - so long as they are not being threatening or harassing, themselves.

what free speech really means is that the government needs to back off, that it shouldn't pick a side, and that it's neither there to police nor protect free expression: this is up to us, as citizens, to work out.

so, as a free speech activist, what i want to see is protestors yelling down ann coulter while the cops sit quietly and watch. should the yelling turn to violence, she would then deserve protection. but, she does not have the right to be heard over the crowd, if the crowd decides otherwise - she only has the right to be drowned out.

in order to gain control over the space, she would need to be asserting property rights, which is a different concept than free speech. once she is in a private space, she can use private security to assert her privilege - not her right - to be heard in a space she has property rights over, or that an owner is asserting property rights over on her behalf. and, i actually don't like that, either, but i'll respect it as the existing legal order in most cases.

generally, a public speaker would not have these kinds of property rights at a public university, and should not, either. the public university should be seen as a state institution, and should not be regulating expression one way or another.

so, again: if you have a speaker at a public university being drowned out by protestors, then that is not a violation of speech rights but an expression of it. if you disagree then, at best, you're confusing property rights with speech rights.

the only way that a speech violation can occur here is if the police come in and try and control the situation, as the government is then taking a side in a debate that they are obligated to avoid taking a side on.