How to placate a very angry priest?

Opening the console, clicking on him, so you see his ingame object id, then typing disable then enable seems to have solved it.

Using setav aggression 0 didn't seem to have an affect.

Although there is already an accepted answer, it relies on console commands, which are not available to console players (ironically).

You can try using a Calm spell, which "reduces the target's inclination to attack for 30 seconds." However, the spell is level-dependent so you may not be able to use it on this particular NPC. You will of course also need access to the spell, through skill training or a scroll or staff.