I've been working on a 5E Glorantha conversion; it's reasonably straight forward. The biggest changes have been to the Cleric spell list, it's pretty much unique per deity. Oh, and the addition of a Shaman class and the excising of the Druid (can't think of a place it'd fit without twisting it around). Glorantha is so very very big, though, I'm pretty much doing *example* faiths and then if my players want to play a, I don't know, Uleria initiate or cleric, I'll write it up then.
I've decided being an Initiate is a feat, like the Magic Initiate feat but a bit more limited (you have to renew your spell at a temple, but the spell can go up to 4th level based on your class level). Other minor benefits are also included, like Sense Chaos for Storm Bull initiates.