A commenter writes, on the campaign finance speech restrictions post,

Although suppression of speech has become a liberal monopoly, John McCain is one with the liberals on this, and he would readily appoint judges who would extend the range of suppressed political speech.

Let me say it again: Conservatives and liberals are both willing to restrict a considerable amount of speech (sometimes quite correctly, I might add). Neither side has a monopoly on speech restrictions. Consider, for instance, my study of how the Justices voted on free speech cases, 1994-2002, which counted their pro-speech-claimant votes, with some adjustments that I explain there (the cases since 2002 wouldn't, I think, affect the bottom line much):

Some conservatives have broad views of free speech protections, some don't; likewise for some liberals. My sense is that the same true for politicians and academics as well.

What if one limits this just to expression that is generally seen as being on core political, religious, and social matters, and excludes, for instance, pornography and commercial advertising? I don't have the numbers on that, but I can talk about the big picture:

1. Conservative Justices tend to be more willing to protect some sorts of such speech, for instance paid-for speech in campaigns, speech by judicial candidates, religious speech within generally available government funding programs, or antiabortion picketing (though note that on this last one, even Chief Justice Rehnquist supported restrictions).
2. Liberal Justices tend to be more willing to protect some other sorts of such speech, for instance speech by government employees, speech that reports on the contents of intercepted telephone communications, and anonymous political speech (though note that on this last one, even Justice Thomas supported protection).
3. On other matters, the views tend to be split, for instance on flagburning (and before you say that flagburning isn't literally speech, remember that contributing money to candidates isn't literally speech, either).

So as to some kinds of speech, left-right generalizations are in large measure accurate, especially when one focuses on Supreme Court Justices. But if we're speaking of speech more broadly, or even just political speech, one can't claim that speech restrictions are the special preserve of either side.