So you're suggesting they don't have separation of church and state in TOS' political system? The Federation Council is a political body.
Okay, so she's not the Pope. But both Vulcan and the Federation could have total separations of church and state, as we secular fans would hope, and T'Pau could be a secular philosopher or former official not currently holding any office. She could be a former legislator or a former member of a president's administration.
She could be a justice on the Vulcan Supreme Court, which makes more sense in that she's officiating at a wedding and judges do that.
But I don't think it was ever said that she runs the whole planet.
I can't imagine that a sitting head of state would ever fly out to the sticks (or the Stonehenge) to referee a fight.