How are Religion and Culture linked?

Lot of questions boiling around here, but the primary one seems to be: "How are culture and religion linked?"

And the short answer? They're not!

Every character and county in the game has both a Culture and a Religion. Neither of these are set in stone -- characters can convert to any religion with the appropriate piety cost (or that of their spouses, for free), and landed characters can adopt the culture of whatever their realm capital has.

The culture and religion of a county can be changed to match your characters via the council -- your realm priest (for Religious Conversions), and your steward (for Cultural Assimilations).

There is no threshold for effects on either of these -- both characters and counties only have a single religion or culture, and in the case of using your Councillors, all progress is lost if they switch to a different task.

Given the opinion malus for having differing religions / cultures, it's often in your best interests (or those of your vassals) to convert counties in your realm to match your own culture.