Any tips on religion in Stronghold HD? Is it any good at keeping people happy?

I have been playing Free Build mode, which lets a lot of room to experiment. During the campaigns there are always some restrictions, special events or threats which add extra difficulty to get the most out of your buildings and peasants. I decided to make people superhappy without even needing to pay taxes, and I maximized food and ale coverage, but religion is another matter. 15% of my population (24 out of 160) are priests. I have built many chapels, some churches and a cathedral, but I can barely manage to get over 50% religion coverage. They are so inefficient! Compared to other happiness sources, such as inns, seems like a waste of resources.

Should I even try to get 100% coverage?

Only if you're out of other options, I think. You definitely need a lot of churches etc. to make any use of them, because priests aren't very keen on patrolling the castle. But hey, whatever helps you raise taxes....