What relevance does The Crucible have to today's society?

Interesting question! One of the things that makes "The Crucible" a classic is that its context remains as pressing today as when it was written.

It is important to remember that Arthur Miller based his story and his characters on real people and events that occurred in Salem, Massachusetts in the 1690s. He wrote the play in response to the Communist "witch-hunts" of the late-1940s and 1950s. Miller wanted to address the paranoia, the ways in which the political mainstream vilifies those who think differently, and how conformity can breed fear and prejudice.

Let's apply that to our own time. I will use the political rhetoric in America as an example. Islamophobia, or fear of Muslims, is a common tool used in politics.

Arguably, there has been a tendency to regard Muslims as enemies to American ideals, as a dangerous "other" seeking to infiltrate the country, do us harm, and, ultimately, impose sharia law. Such views are rampant in some European countries as well. These awful prejudices are identical to those that Americans had toward Communists in the post-war period; and similar to those that many Puritans had towards those whom it suspected of witchery.

Consider, too, the characters of those who were suspected of witch-craft. In the play, John Proctor is accused of witchery because he refuses to participate in the witch-hunts; thus, he is a non-conformist, which is always deemed suspect and, possibly, dangerous. Giles Corey stands in the way of Thomas Putnam's business interests, so, ultimately, he is killed. Corey's wife, Martha, is an easy target for Putnam's manipulations to secure Corey's land because she reads what are considered strange books -- books that are incompatible with Puritan values. 

The play's attention to political oppression and to the fear of those outside of the mainstream make it as relevant today as ever.