How common were power struggles between King and Church in medieval

Very common.
John Lackland was pretty much beaten by pope Innocentius III. His desperation resulted in the Magna Carta.
Many French and German rulers created Antipopes to try and get some leverage.
The pope was generally supreme.
The church was the single largest landholder in western Europe, and the pope had more wealth and influence than any western monarch. On top of that the Pope is the one who both appoints Kings, and the one who can threaten your afterlife via excommunication (this was a big deal).

On the flip side we have the Byzantine empire and eastern European countries that were influenced by it.
Here we see caesaropapism.
The Emperor is above the church.
The patriarch of Constantinople was still a very powerful man. The empire generally tried to keep the state and church on the same side. To present the state and church as one entity (DOUBLE HEADED EAGLE, DUDE HERALDRY LMAO)
Notably the Byzantine Emperor meddled directly in the elections for the Patriarch as he named one of the candidates (who better be the winning one), while the Pope was elected by cardinals (corruption here was notable, but not so much from kings, more like wealthy merchants Alexander VI bribed his way into his position).

Very common, you essentially had two powers in every country which vied for power. The church lost in the end.

Becket is less a case of church vs state and more asshole vs state. The guy was just a fucking prick, every compromise he shot down, even the Pope thought he was a little bitch.

Don't know how big of a meme it is but afaik the Pope sanctioned the Norman invasion of England because the anglos were appointing their own bishops and Stigand for one paid homage to an anti-pope and the normans basically promised to be good goys if they got the papal banner for conquest

>>1520680
did the ERE celebrate the same festivals and public holidays as old Rome? or did that change when they converted to Christianity?

>>1520717
They celebrated the same festivals.
The timing of Christmas and Easter have nothing to do with Christianity, rather with Roman festivals.
Christianity as we know it today was shaped by Rome. The cult of Isis had a great influence on how we see Mary today.

>>1520680
this is why england almost converted to islam way back in the 13th century, waaay before 2012.

It happened continuously.

Starting with the Cluniac Reforms in 910, the Church started becoming a political power. There was the Investiture Controversy which opposed the Papacy to the Holy Roman Empire for half a century. It ended in 1122 basically with a victory of the Church, marking the beginning of the fall of the HRE. Then as France rose to being the main power in Europe and the French king started expanding his authority, that eventually led to a conflict with the Church around 1300. That went very differently though, the French king had the Pope kidnapped, a French Pope elected in his place, and the Papacy moved into France. Where it stayed for a century until the Hundred Years War weakened France too much.

After that the Papacy had lost most of its power though and was no longer a major political force.

>>1520742
Vladimir the great chose to convert the Kievan Rus to Orthodoxy over Islam because he didn't agree with the ban of alcohol and pork.

Sort of tangential, but I remember reading somewhere that early King Arthur stories would sometimes put him into direct conflict with the Pope. Any truth to that?

>>1520759
He shows up briefly in Le Morte Darthur to scold him for the war over Lancelot and Guinevere's adultery.