To use a well-worn phrase, I beg to differ with the previous answer. The conflict between Becket and Henry II had everything to do with conflict between church and state. When Henry maneuvered Becket into the position of Archbishop of Canterbury, he thought he was putting his puppet in the highest church seat in the nation. With his good friend Becket in control of the church, Henry would have his way.
However, that was not the way things turned out. Thomas Becket actually took his position seriously. When Henry wanted Becket to rule in favor of trying priests who commit crimes in civil rather than religious courts (where they might just get a slap on the wrist and reassignment rather than a harsh sentence), Becket stood firm in his belief that the state had no authority over the church and its priests. Becket even went so far as to excommunicate two bishops who sided with the king and opposed him. Becket frustrated all of Henry's plans.
It is ironic that another Henry only 400 years later did exactly what this Henry had wanted to do when Henry VIII declared himself head of the church in England.
The story of what happened between Thomas a Becket and Henry 11, King of England is certainly tragic, and the themes and causes that run through it certainly have roots in religious issues. The rise,then fall, of Thomas from the friendship of the king bears all the hallmarks of pity for his plight and fear for ourselves in similar circumstances - many regimes even today demean or even persecute citizens for what they believe. We also have a 'hero' type figure, someone who is brave against some kind of conflict or odds. Even though the piece is written in verse, it can still be called drama, so many of the elements of a 'religious tragedy' are there. Religious or spiritual themes are strong too, and the argument of the church or the divine against the state still rages on today. In Ireland the church was accused of actually being the state, for example, and is still accused of influencing decisions such as whether to join Europe with the Lisbon treaty.
Drama ? Yes
Tragedy? In terms of what happened on a human interest story level to Thomas, yes too. Biut in terms of the delineation of church/state, some might not think so!
NB Yes, of course! The 'some' refers to The Church Of England, The Church Of Ireland, and Henry V111 - the debate goes on.... tha's one of the things that makes this skilled verse so timelessly relevant.