A good time to follow the rule "historicize the thing." In 20th Century US there are periods when the claim "many non-communists defend the civil liberties of communists" is false (1917-1919) (1949-1953), and periods when it is true.
In the first category - when repression really hits - you have judicial civil libertarian icons like Oliver Wendell Holmes and progressives like Nuremberg prosecutor Robert Jackson justifying, in the first case, the jailing of Eugene Victor Debs for purely political speech or, in the second, shittingallover [Flemings proof?] the first amendment and screeching insanely about communists in the labor movement in ACA v. Douds. The failure of even the ACLU - which had been created in response to the repression of 1917-1919 - to defend the civil liberties of communists in 1949-1953 was total. This failure arose from what was described - proudly - at the time as "anti-stalinism", which led skilled first amendment lawyer (he litigated the "Lady Chatterly's Lover" obscenity case) & labor oriented progressive ACLU head Morris Ernst to an extensive personal correspondence with J.Edgar Hoover in which he suggested targets for the FBI's attention. If it comes round again this is a trajectory, I fear, that will be followed by some of the people that for instance Nathan and Justin know today and think highly of. In the 1917-19 period when the IWW was smashed by all tactics from mass summary trials to lynching, you can count on your hands the number of non-left socialists - non-communists would be an anachronism - who *at the time* even spoke up for (let alone "defended") their civil liberties. Roger Baldwin and damn near no-one else. See cold war liberal (though he grew out of it a bit in the 1970s) Paul L Murphy's *World War I and the Origin of Civil Liberties in the United States* (Norton, 1979).
In the second category - periods without acute repression of the revolutionary left, self-described in 1920 by the rulers as "normalcy" - it is true that many non-communists have defended the civil liberties of communists, though more would of course be better.
Max, did you really get to cite Monthly Review on Fox News?
john mage