I was going to write that liberals do not want to shut down free speech, but as I looked at the existing answers, I saw that there was some truth in the claim behind this obviously trollish question.
Here is the real answer: Everyone wants to shut down free speech for people they disapprove of. It’s a human thing; we all want concord at some level and are very uncomfortable with discord, especially regarding important values.
That is precisely why we need to have an explicit right to free speech that is protected by clear language in the highest law of the land. In the U.S. we have the first amendment to the Constitution to articulate and protect the right of free speech.
It is not conditional. As soon as I write that, I must observe that there is some speech that is not protected: One may not advocate the violent overthrow of the government, for example. There are other cases, but I am not a lawyer, so I will leave their enumeration to others.
When I see that people advocate free speech, providing that it is properly used: That it does not directly insult or demean people, then I can see that the troll who posted this question happens to be right. Many people who call themselves liberals do want to shut down free speech for racists, climate-change deniers, and others whom they regard as dangerously aberrant in their utterances.
Perhaps that would result in a more civil public discourse, and God knows we could use such a thing, but then we would no longer have a free society in any seriously meaningful way.
The price of freedom is that we must tolerate racists, morons, and complete assholes, and let them say what they wish to say. There is no alternative to this, and there are no moderating rules of any kind that will not lead to the destruction of our freedom.
Public safety considerations make it necessary to ban certain speech, as mentioned above, and as long as these exceptions are perfectly clear and very few in number, we will retain our freedom.
But when we try to make the case that abhorrent thoughts lead to abhorrent speech, which leads to abhorrent actions, then our freedom will be short lived because we will outlaw the speech. We will do this because thoughts cannot be seen or heard, and thoughts are what we really want to outlaw.