Priest do convert people to christianity in any region they are in. A priest or a church will slowly convert the people in the region it is in.
So, like Shinobi's, you can use a couple of them to create revolts in other Clan's territories. This will be buddist revolts, containing WM, so you can cause real trouble with it. But there's one problem, priest are very easily killed by ninja's. And there's no way to protect them in enemy territory.

IIRC - a Cathedral doesn't only convert in it's own region, but in all regions owned by the Clan that owns the Cathedral.

When I converted to christianity, I built a church in lots of regions, in the ones I didn't have one, I had a priest. After a couple of years I managed to convert the entire population.

I think a Buddist Temple in a region does work the other way around, if there are any christians in the region, they may be converted. But this goes automatically as well I believe. If there's no army, no buildings in a region, if there are any christians in it, they will turn back to Buddism.

But it never occurs the other way around, iirc.. people are never suddenly converted to christianity if the region is owned by buddism, there's no church or priests in it. However as soon as you accept the portugese offer slight parts of the population turn christian, following your example.

I've been involved in some situations regarding all this in the past, so I'm pretty sure of it. However not for the 100%, it's been quite a while ago I might not recall correctly what I experienced.

Gah! in the coming holidays I'm going to play some STW again, it's about time. been way too long ago since my last campaign.