Nearly every race in the game can be a Priest, and nearly every race has its own distinct ‘priesthood’. The priest identity problem was put under a magnifying glass in Legion when the Order Hall had to be reduced down to having a LIght and Shadow side because the exhaustive task of representing each unique school of priesthood could only be done by showing off NPCs with the titles and appearances you might’ve expected.
It’s different for the Shamans and the Druids, though. Despite the fact that those classes are unified under mostly the same fantasy (druids belonging to the Cenarion Circle and Shamans belonging to Earthen Ring, both of which have been multi-racial groups since before they were prominent in Cataclysm).
If the races of Shaman and Druids can get race-specific visuals despite the fact the lore is hardly different from one another, it seems reasonable that there could be racial visuals for a class where nearly each race is distinct from one another. Just to lay it out:
Human, Dwarf, Gnome, Dark Iron Dwarf: Brotherhood of the Light
Night Elf: Priesthood of Elune
Draenei, Lightbound Draenei: Worship of the Naaru
Void Elf: Void Worship (no indication if they can even use the Light outside of game mechanics)
Troll/Zandalari: Loa Worship
Forsaken: Cult of the Forgotten Shadow
Tauren: Seers in reverence of An’she
Blood Elves: Purification by the Sunwell
Goblins: Brotherhood of Light or Church of Chance (no other distinct faith has ever been mentioned)
Pandaren: Reverence to the August Celestials
There doesn’t need to be racially unique spells like there were in Vanilla because those were a balancing nightmare, but some new visuals would be great. There’s an actual lore backing why these priests are different, it’d be nice if they felt different as well.