This play is about the disturbing nature of historical change rather than the events themselves. Monarchs have always had to watch their backs for fear of ambitious family members who want to sit in their plush thrones. Shakespeare makes note of the importance (self inflicted or otherwise) of the royal status with the gorgeous tournament staged in Act 1 scene 1 and also Richard's rhetoric on the divine right of kings in Act 3 scene 2.
In this play, a potentially successful government has been created, but the cost of it is the erosion of spiritual beliefs which in turn is the catalyst of civil disorder. The people have depended for so long on social order with religion front and center. The deposed king had failed to serve the people and the new king had been sent by God to do so. Within this logic is the delicate situation which illiminates not only the inadequacy of the conquered king but also of the successful rebel. An ironic piece of the royal puzzle, as shown in this quote from enotes:
Bolingbroke sees that Richard’s incompetence is hurting England. To rid the kingdom of a ineffectual monarch, however, he must do further damage by overturning the law and claiming a throne to which he has no clear right, acts that will eventually lead to decades of turmoil.
Therein, methinks, is the tie to the Reformation. Follow the link for more information!
The following quotation from eNotes (link below) might best describe how Reformation ideals influenced Shakespeare:
Shakespeare...painted a masterful portrait of a tragic character, a weak, self-centered king who loses his throne to a more practical and decisive man but who nevertheless evokes sympathy for the suffering he endures. As Richard’s emblems of kingship are stripped away, he is forced to recognize that he is no longer a “native king” but merely a flawed human being.
The play centers around the real struggle between cousins Richard II and Henry of Bolingbroke over "the divine right of kings." Richard embodies the idea that kings are ordained by God and that only God can judge them.
The Reformation in England was more about politics than about religion. Henry VIII wanted to marry Anne Boleyn, and the pope would not grant him a divorce from Katherine of Aragon. So Henry broke with the pope, declared himself the head of the Church of England, and married Anne. So in a different way, Henry VIII (and his daughter Elizabeth I) embodies the divine right of kings.