Religion is at the heart of A Man for All Seasons: Basically, Thomas More doesn't want to change his religion or betray it or compromise on it, and virtually everyone else wants him to. They end up killing him for it.
In order to get a divorce and get remarried, King Henry VIII needs to break with the Pope. And, corrupt as the Pope of the time may or may not be, More sees him as the right representative of Christ's Church on earth: To question his right to approve marriages like Henry's would be treason against God.
Questions About Religion
Is Henry VIII breaking with the Church for purely worldly reasons—or does he have an honest religious beef with it?
Does religion matter to More's opponents, Cromwell and Rich? What about Norfolk?
Why won't More break with the Church and follow Henry? What is it that compels him to hold onto his belief in it?
Does More think he will be damned if he signs the king's oath?
Chew on This
If you're Thomas More, you believe that the institution of the Church really matters. Christ established it and put St. Peter in charge. You can criticize problems within it, but you can't attack the institution itself. That institution is definitive and God-established.
But, if you're Thomas Cromwell, you don't see the institution as that important. For Cromwell, the institution of the Church is far less important than his more personal form of belief.