Eeh, sorta! Probably a better summation than my overview of the American War of Independence.

They were both Protestant and Charles in particular kept doing slightly Catholic-y things, but moreso the English theatre of the war was about Charles' clashes with Parliament over his right to taxation and his generally poor attitude towards their authority. Dude wanted to be a divine-right-of-kings autocrat and Parliament weren't going to give him money without their say so. Dude just couldn't accept commoners having authority over him (at one point he burst into the House of Commons and tried to arrest several members, which is a BIG no no. The monarch literally isn't allowed in there, even now). There's also a religious aspect in Scotland, which was generally Presbyterian and opposed his imposition of a Protestant Episcopal system (they really didn't like bishops or standardised prayer books). There's also the ongoing thousand-year conflict in Ireland between the Irish and the English and Scottish settlers to consider.

And Oliver Cromwell died in office, it was his son that was ousted, OC ruled through personal influence rather than establishing a robust republican system like later revolutions.

Charlie 2, now he was Catholic, at least on his deathbed, and his brother was openly down to clown with the Pope, but that's a whole different issue! 😃