Small H/P hits. Literally EXACTLY like vulgarity. A button you can click on every message a person sends (even to non-members of the religion or private messages) that will refer the message to a selection of elders and/or priests of the sender's religion. However the internal vulgarity mechanic works, duplicate it and, if the message is ruled vulgar, then, bam– they take a very slight H/P hit. Maybe even make it generate an in-religion notification, "Rumors that So-and-So has been making unorthodox and unsettling statements have begun to spread..."
Actually, if Oratory was a purely priestly skill and not mixed with other non-religious actions, I'd say you should get a hit to Oratory and not to H/P. But this is probably too complicated to unentangle by now.