Great question! It needs a little reframing though, because it assumes (in a typically post-Enlightenment way) a clear distinction between the realms of politics and religion. That distinction doesn't exist in this context: political theories such as divine right are explicitly theological, the Anglican Church, the only legal church, in turn is appointed by the King. There is a constant link between throne and altar, the King promotes the true Christianity and true Christians obey their King.

So in this environment are persons religious convictions have politial connotations, just as their political views have religious ones; the categories overlap so much that they're indistinguishable. Sometimes priorities that you and I would categorize as "religious" shift people's "political" views, and vice versa. It's complex, so I'll offer an example. I regret that I don't have access to my books, so I can't offer exact quotes, but everything here is taken from 1688: the first modern revolution. I can't recommend that book enough, it's of the highest order of quality.

The Stuart family was afflicted by Popery. Charles II, restored as King in 1660, pursued an unpopular pro-Catholic foreign policy but always personally upheld the Church of England. Charles II and his younger brother James, Duke of York, had been exiled in France during Cromwell's years. In that time they'd received financial support from the French crown, fought under French colours, and been duly exposed to Catholicism. This plants the seeds of affection with Catholicism and French Catholicism specifically.

For his entire reign Charles II fights Parliament to maintain his pro-French policies and receives giant top secret subsidies from Louis XIV. In 1668 James, the heir to the throne, secretly converts to Roman Catholicism. He does this for very interesting reasons. Having spent his youth fighting for his right to rule, he has examined the religious justification for secular government, and decided that on that basis of divine right Martin Luther had no just cause to rebel against the Pope way back in 1517. For James his developed political ideas have religious implications, they're in tandem with his Francophilia, so it follows that he secretly converts.

Being a secret Catholic is a political bombshell that involves the whole family. Anti-Catholic measures are consistently popular with Parliament. We're only a few decades after a war between Charles I and Parliament. Having the heir to the throne be a crypto-Catholic is a threat to the succession. The first thing Charles II had to do was order James' daughters (and heirs) be raised Protestant. Eventually you can't even keep the dark secret, in 1673 Parliament comes up with this Test Act for all state officials to deny Catholic doctrine and diss the Pope. Being the principled man he is James resigns, now his Catholicism is public.

Everyone is very angry and 3 successive Parliaments try to introduce bills that James won't be able to inherit the crown. Charles II keeps dissolving these angry Parliaments, but he's getting older and has lived a hard partying life. There's some perverse good fortune for James though: some of the Protestant radicals go so far as to concoct a republican plot against the life of James II. That's terrifying for Tories who supported a monarchy to try and reestablish normalcy in property rights and goes a long way to alienate even Whiggish gentry. The right of Monarchy is after all a right of property inherited!

So when Charles II dies in 1685 James is able to become James II on that surge of support. The nation now has something it hates, a Catholic King, but there's an early rebellion against James by the Duke of Monmouth, illegitimate son of Charles II. Monmouth's rebellion is explicitly Protestant and anti-Papist, it founders and is crushed by James II. All the powers that be are plainly willing to support the new Catholic King for the time being, a purely religious appeal is inadequate to sway them.

James II is famously overthrown by William of Orange in 1688, 3 years after his execution of Monmouth. I've typed enough for now, but if you're interested in any of this the first thing you should read is Pincus. I'm very interested in this period and would be happy to offer more reading suggestions or answer any further questions I can.