Henry was in the right!
Being old enough to remember 1964, I can tell you the Catholic Church was gaga over this movie at the time. A man who is a moral conscience to the King to start with, and then finds a new Master who is more demanding...and more satisfying to serve.
And it's a very good movie, particularly if you can't hear Richard Burton's rolling Welsh accent enough, and enjoy watching him act before he started in on his series of humorless, self-loathing characters in movies with bad scripts. In contrast, Burton's character here finds real inner peace before his death.
The thing is, what splits Becket and the King? A priest is accused of molesting a subject. Becket wants him tried by an eccesiastical court, the King by his own magistrates.
Considering the sex scandal that has enviscerated the U.S. Church, especially the revelations of Church wrist-slapping of guilty priests, who can doubt that King Henry was in the right? No one today would advocate clerical immunity to civil authorities.