You are correct that all of those are rights. The question here is what is the course of action that will lead to the best outcome?
People who believe YC should disassociate from Thiel are doing so based on the belief that the consequences of not doing so would be to promote a Trump presidency, which would have bad consequences to a variety of minority groups, etc.
People who believe YC should not disassociate from Thiel (I am one of them) would assert that doing so would set up or perpetuate a norm in which it is acceptable to ostracize people for unpopular opinions (unpopular relative to a certain community or context). Brendan Eich was another semi-recent example of this.
The effect of this, I believe, would be to: a) further balkanize and polarize our politics, and b) to exert chilling effects discouraging people from airing unpopular opinions, which in turn would inhibit an open marketplace of ideas, which, I believe, is necessary for progress. I believe individuals and societies can only grow by being exposed to a variety of ideas, some of which they disagree with, and ostracizing people who disagree would prevent this from being possible.
So both sides are arguing there are negative consequences they are trying to avoid. Which side an individual will come down on, I suspect, will depend on how much weight they place on each type of negative outcome.
As a personal aside, I know what it is like to have to be ostracized for holding an unpopular opinion. I am an atheist in a deeply red and religious state. I have tried to "come out" and quickly had to "get back in the closet" based on the intensity of ostracism I received. So I admit this kind of thing has made me more sympathetic to people holding unpopular opinions.
In any case, I don't see anyone denouncing the right to protest, just the protest itself, which is the next turtle on the way down from your sentiment.
Shouldn't individuals have a right to have terrible opinions?
Of course they do. But a surprising number of “free speech” and “free market” people don’t seem to understand how either works.
Individuals have a right to support white nationalists.
Individuals also have a right not to do business with those who support white nationalists.
Individuals also have the right to organize protests against those who support white nationalists.
Let's be clear: defending the right to support a white nationalist while denouncing the right to protest against one isn’t courage, it’s sophistry.