COMMON MAN: (Rises) It is perverse! To start a play made up of Kings and Cardinals in speaking costumes and intellectuals with embroidered mouths, with me. (1.2)
Quite a way to kick things off, huh? Common Man's amusing adjective switcheroo aside (put "speaking" and "embroidered" in each other's places to understand this one), this opening line tells us exactly what to expect from the play. As you'll see, all those politicians and bigwigs aren't exactly good dudes, or anything like that. Have they ever been?
MORE: But, Richard, in office they offer you all sort of things. I was once offered a whole village, with a mill, and a manor house, and heaven knows what else. (1.66)
In 16th-century England, bribery is so common among politicians that it's pretty much an official business practice. That's a big stinkin' problem, Shmoopers. If we were to explain it by means of a math equation, we'd say that politicians + corruption = bad times for everyone who's not a politician.
WOLSEY: Let him die without an heir and we'll have them back again. Let him die without an heir and this "peace" you think so much of will go out like that! (1.228)
Henry's desire to divorce his wife is more than a personal issue. It's more than a moral issue. It's more than a religious issue, even—it's a political one. Henry's the stinkin' King, after all, which means that his family drama has the potential to throw an entire country (maybe even a whole continent) into chaos.
CHAPUYS: Ah. (Mock interest) But then why these Justices, Chancellors, Admirals?
CROMWELL: Oh, they are the constitution. Our ancient, English constitution. I merely do things. (1.404)
In other words, Cromwell is like that shady modern lobbyist who works backroom political deals with little regard for silly things like laws and regulations. That's what makes him so evil in comparison to More. While More follows the law to the letter, Cromwell just crumples it up and throws it away.
MORE: (Eagerly) Then why does Your Grace need my poor support?
HENRY: Because you are honest. What's more to the purpose, you're known to be honest. (1.566)
Basically, Henry knows that More's refusal to acknowledge his divorce is really bad P.R., and even though the dude doesn't have to run for election, he still wants to have a stable, easily controllable political environment. Getting More to change his tune is going to be a lot easier said than done, however. Also, note that honesty itself isn't really the issue when it comes to politics—it's the appearance of honesty that matters. You don't need the truth in politics; you just need truthiness.
HENRY [...] There are those like Norfolk who follow me because I wear the crown, and there are those like Master Cromwell who follow me because they are jackals [...] and there is you. (1.566)
Let's break this one down. Norfolk is the kind of dude who follows the existing political order blindly: he follows Henry because them's the rules. Cromwell is the kind of dude who can see through the political order and who uses that insight for his own corrupt benefit. More, on the other hand, is a different beast entirely: he follows his own conscience above all else.
CHAPUYS: My Lord, I cannot believe you will allow yourself to be associated with the recent actions of King Henry! In respect of Queen Catherine.
MORE: Subjects are associated with the actions of King willy-nilly. (2.51-52)
It's worth noting that More is hardly the rebellious type. He seems to have a strong amount of respect for Henry, and he never does anything to subvert the King's authority. That's why he gets so annoyed when Chapuys bursts into the scene and tries to make it seem like they're political allies. They might follow the same religion, but More is still a loyal British subject.
NORFOLK: Yes! Crank he may be, traitor he is not.
CROMWELL: (Spreading his hands) And with a little pressure, he can be got to say so. And that's all we need—a brief declaration of his loyalty to the present administration. (2.174-175)
Here's a pro-tip, with the 20/20 hindsight of history: making people take loyalty oaths is always a bad idea in the long run. Not only does it lead to the deaths of people who don't deserve to die—like More—but it also represents an frighteningly authoritarian impulse that could easily snowball into something far nastier. Not a good look for anyone involved.
COMMON MAN: [...] "Thomas Cromwell was found guilty of High Treason and executed on 28 July, 1540. Norfolk was found guilty of High Treason [...] on 27, January 1547." (2.459)
The two men who got Thomas More executed for treason (a crime he didn't commit) end up getting convicted of treason themselves later on in the game. Funny how things work out sometimes, huh? In an even juicier bit of gossip, Cromwell was also supposedly responsible for the execution of Anne Boleyn—the woman Henry divorces Catherine to marry.
MORE: That's very neat. But look now...If we lived in a State where virtue was profitable, common sense would make us good, and greed would make us saintly. (2.609)
Dang—leave it to More to lay it all out on the table like that. Basically, More knows that the British political system is corrupt as all get-out; you'd have to be blind to miss that. But that doesn't mean he'll let the system corrupt him, too. Unlike most people, More sees the immoral political actions taken by his peers as incentive to be a better man himself.