I've been meaning to post something about this for a while, and The University of Oklahoma's SAE Fraternity and the Limits of Free Speech is my tipping point. The people who want to restrict speech in the belief that it will help marginalized people--brown people, queer people, trans people, etc.--are not leftists, because those are not right or left issues. Log Cabin Republicans and Libertarian Party members and sane Republicans support those rights, as do most Democrats and every socialist and anarchist I know. Obama, whose politics are right of center, supports those issues. They are centrist issues.
These people who want to limit speech are the modern Reverend Bowdlers and Mrs. Grundys who want to impose their vision of niceness on everyone else. They're not on the political right, but if they're not promoting anything left of the Democratic Party, they're not political leftists either. They're just authoritarians, no different than the Maoists and McCarthyites of the last century.
Among the many things they do not understand is that a right to free speech is the only thing that guarantees marginalized people may speak.
Recommended: I BELIEVE IN FREE SPEECH, BUT… by Kenan Malik