This was the McCarthy era where censorship was the name of the game. In fact, McCarthyism has become part of our vocabulary as it refers to the act of accusing people of disloyalty, subversion, or conspiracies without the need for evidence. This took place in the late forties and fifties in America at perhaps the height of the fear of communism.
The intellectual community was hit particularly hard. This should not be surprising, because those in power are always fearful of independent thinkers. Some of Arthur Miller's were charged as well as other prominent scholars. Hence, the Crucible explores the same dynamics as McCarthyism, but in a different context. Witch hunt then and now is the point.
During the 1950s, many Americans worried about the influence of communism inside the US. So HUAC held hearings about it, partly for political reasons, partly to make themselves look good, partly out of real fear. People could be brought before these hearings or other "loyalty" tests just because they were suspected of being communist or because someone said they were communist.
This is pretty similar to what Miller is talking about in The Crucible. In the play, people are accused of witchcraft not because of any real evidence but because other people don't like them or because there's just this mass hysteria going on.
This is what many people see as a major similarity between the two.