We also learn much from the Common Man in the play, and unfortunately it is very easy to be like him. Indeed, the Common Man represents all of us who change our values to suit situations (just as he changes clothes to play one role and then another). Many of us, too, are like Henry, very vain, ready (metaphorically) to dance and show off our legs as does he to prove himself to Margaret when he visits More. If anything is striking about More, it is humility, for he would happily go into obscurity to keep his conscience clear of falsehood or violating his integrity. He is not interested in taking on Henry in a debate; in fact, he tells his wife, “I neither could nor would rule my King. . . . But there's a little . . . little, area . . . where I must rule myself,” and that is what he refuses to give up, that “little area” that is his conscience. So in asking if this is relevant today, we need to consider who has such strength of character, whether in small incidents (peer pressure to do this or that), or in large ones (political pressure to vote for or against a measure in congress, not because it is right but because of lobbying or political favors).
I believe this play does have relevance in any society, in any time period in history, including today. Ultimately, once you break past the constraints of the Tudor society and politics it is specifically discussing, it is a play about conscience and doing what one feels to be right and moral, rather than bending under the pressure of a government or a best friend.
Sir Thomas More, though a dear friend and supporter of Henry VIII, could not condone the idea that Henry was going to divorce his wife, Katharine of Aragon, in order to marry his mistress, Anne Boleyn. More was a devout Catholic, and says right before his beheading, "I die the king's good servant, but God's first." (I believe that to be accurate from the play - I'm not sure if it is historically accurate, but it does definitely illustrate the character of More.)