Down here, the registry offices will let you take a few discrete images during the service, with no flash, but they go mad if there is a constant shutter click going on, they also ask that the guests take no pics during the service & to respect the right of the paid photographer to obtain the images they require before flashing every where !!
Churches are so varied that its a case of finding out from the priest/vicar etc what they do or dont allow. Some churches now charge extra for the right to take photographs during the service, but will allow you to capture the entry of the bride & the signing of the register.
The maddest place I have been is in St Nicholas church off Old Town Square in Prague, I was being the normal reserved Englishman & the local Videographer was up on the altar behing the priest with a 500watt lamp on the front of his camera... I got a few usable shots, but he was burning me out !!!:bonk: