As a general rule, I think you are right though I would add profession to location and race. Within a pantheon, people tend worship the gods who represent the things they hold important in their lives. Farmers worship Barntar or Orlantha the Farmer, hunters Odayla, merchants Issaries, etc.
But general rules are made to be broken. In cultural border regions, there might be more competion. The EWF and God Learners intruding into lands with traditional Orlanthi for example. In 3rd age Glorantha, the Lunar cult of the Seven Mothers was presented as a missionary cult.
I wouldn't penalise priests for healing characters who are not members of their cult. But if you think it fits with your picture of the world, then you should do so. Maybe if they heal a member of a hostile or enemy cult, they have trouble getting the spell the next time they pray for it. Maybe it is a problem only for some cults. Chalana Arroy will likely be more generous than other gods.