Once you get into the High era (after 1205), the best way to deal with Catholic factions is to train up a legion of Grand Inquisitors and go after the faction leader. I find the normal Inquisitors just don't have any chance of success against even an Atheist Faction leader (sitting in a 100% Zeal province). Once the faction leader dies, find any heirs and burn them as well. Eventually the faction will run out of heirs and they'll go rebel. At that point you can bribe or invade without worry.

This tactic won't work against the HRE (as they elect their leaders), or the Pope.

I was playing as the English and I had to deal with a massive Spanish faction with alot of provinces, a huge mobile spanish army, and heavy naval support. In this case, I ended up eliminating the faction and using my 350K treasury, began to purchase the loyalty of many provinces. Luckily the Byzantines (the only other powerful faction) were devastated by the Spanish, otherwise they would be a problem.

GI's are a great tool to use to take down a faction when you don't want to go to war with them, and that won't also be taken out by annoying border forts.