You've probably heard it before. You'll definitely hear it in the future. And it goes something like this: "God, those liberals are just so intolerant of those who don't agree with them." It may be accompanied by something along the lines of "they claim to support tolerance, but don't tolerate opposing viewpoints." Usually, it's used as a supposedly effective counter-argument, a rallying cry for conservative against liberal ideas. Unfortunately, it's not true at all.
To begin with, "tolerance" and "acceptance" are NOT the same thing. It's one thing to tolerate the idea that homosexuality is a sin. It's quite another to accept it as valid. Tolerance is required by the First Amendment, since everyone has the right to an opinion and free expression thereof. Acceptance is not, because, by the same logic, anyone is equally entitled to believe that those who consider homosexuality to be a sin are wrong. In other words, the First Amendment allows you to freely express your ideas. It does NOT, however, prevent others from also using their First Amendment rights to call out your ideas for being racist, sexist, homophobic, or logically indefensible, if that's how they feel about those ideas. So when people accuse liberals of being "intolerant," what they often mean is that they're accusing liberals of not agreeing with them, which is no crime at all. No one is obligated to respect another's idea as valid, only to respect their right to express that idea.
More importantly, just like any other ideology, American liberalism isn't about accepting every single viewpoint that exists out there. Yes, American liberals support freedom of religion. But obviously, that doesn't come with acceptance of religious beliefs that allow dangerous and harmful practices like human sacrifice, honor killings, and other religious practices that can cause harm. Moreover, it doesn't come with acceptance of beliefs that denigrate homosexuals, women, and minorities. Similarly, American liberalism supports freedom of speech. But that doesn't come with the support of harassment or threats. And it certainly doesn't come with the acceptance of speech that is unabashedly racist, sexist, or otherwise intolerant. We may support your right to express such speech. But we sure as hell don't agree with its contents.
It's become standard fare for conservatives to claim that liberals suppress speech that doesn't agree with their viewpoints. Aside from a few cases of university censorship (for example, these eleven instances), such claims are simply a matter of agreement. Sure, you have the right to express your opinions. But if I deem them to be intolerant or even disagreeable in some way, I also have the right to call them out for what I think they are. It's not 'intolerance' for me to criticize your speech, it's only disagreement. Such free discourse is perhaps the most fundamental of American civil liberties.