Conservatives have been demonstrated in psychology research to have a fairly low tolerance to ambiguity. Basically, they prefer things in black-and-white terms instead of trying to figure out how many shades of gray there are.
They prefer having certainty and clarity, even if it isn't reflected in reality. It's just the way their brains process things. It's why conservative people tend to be far more deeply religious. They drooled over Trump simply because he had no filter: he said exactly what was on his mind. They worship the Constitution because of how unchanging it is.
It's this staunch resistance to change and low tolerance for ambiguity that makes them reject the discussion of topics that challenge the established order. They like having clear boundaries and categorizing everything into neat little boxes. Anything that violates those parameters is seen as abhorrent. A threat to be eliminated. So by making it taboo or by restricting the discussion, they can basically contain the threat and prevent it from challenging their rigid worldview.
It's easy to control the conversation when you silence those with alternative views
