It is the modern liberal that is against free speech. For example, a poll recently
found that 60% of Millennials, who are largely liberal, belive that "hate speech" should be made illegal. Free speech is nearly non-existant on college campuses. There are often what amounts to riots and other efforts attempting to shout down speakers whose viewpoints don't conform to liberal ideology at UC Berkley whose student body is overwhelmingly liberal.
Conservatives tend to not try to impose their beliefs on others, and rely on the belief that everyone is free to make their own decisions. The guiding principals behind the WSJ opinion section, which is very conservative is "Free People, Free Markets", and 'free people' requires free speech.
