If there were regional sectarianism in the Faith, what would the specific traits of each sect of the Faith be?

Good question!

As I’ve discussed earlier, one of the major areas of disagreement I’d expect to see would be competing claims for regional pre-eminence, similar to how the Bishoprics of Rome, Constantinople, Alexandria, and Damascus fought to be recognized as the first among equals. So I’d definitely see whatever the Sept of the Vale is claiming that as the oldest Sept, they should outrank the Starry Sept, and so on.

However, I also imagine you’d see quite a bit of syncretism to local conditions, similar to what we saw with the Ironborn. So I would be very surprised if the Dornish church hasn’t figured out some way to square the circle between the Faith’s precepts and Dornish customs, I imagine you’d see some remnants of Rhoynish religious imagery – the Mother is going to look a LOT like the Mother of Rivers, and I imagine you’d see a lot of turtle icons in Dornish septs. Likewise, given the way in which things like chivalry were imported into the Reach’s legends of Garth Greenhand and his offspring, I would also imagine that the Father in the Reach bares a lot of visual similarity to the green man of the Reach.