I'm just as eager to know as you are, Tex...! I'm interested in the positives and/or negatives re the 'Tifa' faith myself, as a forthcoming Dras healer/alchemist type... However, as yet the Devs are keeping deliberately quiet about the 'religious' professions, and have hinted as such. You've clearly looked at the religious info that is open to us. All I can suggest is that you keep watching...whether on the CoE Wiki or the Discord. Maybe on Discord, Caspian may even be 'baited' into letting some morsel of faith-related secrets out...? Only the God(s) know!
As to how those of different faiths relate...? I am guessing myself that will be partly down to the specific 'situation' that's occurring in game as they meet; I imagine that our own gossip/guile or persuasion skills might also affect that? Myself, I'm even wondering - if my character's build and look might be of a type that makes this remotely possible - if I might even be able to disguise myself in the other 'cults' clothing style or decoration, and 'attend' a meeting as one of them, to find out the difference first-hand! Just a sneaky thought I have (don't tell anyone!)? Good Luc - whoops - I mean, 'May the Blessings of [Insert your Particular Providence] be Lavished upon you...!'