I think this opens the door to the more pernicious old question of how you discover reciprocal initiation in play. If I come to a new jurisdiction where they don't recognize Goldentongue, I need to identify their local equivalent and convince their examiners to let me set up my shingle. This may involve a little lip service to their gods, certification, silver crosses palms, I swear not to handle state monopoly goods and respect local pricing, etc.
I basically have to prove my magic and prove to them that I respect theirs. Once that happens, I was always already in -- their temple is compatible enough with mine that I can recover spells and sacrifice there, I was always compatible enough with them that they'll take me (even begrudgingly). Until that happens, they don't know me and will tend to deal with me like any other interloper trying to horn in on their action.
It's probably similar for many of the other old "generic" cults, many of which perhaps not coincidentally have something like a professional or guild-like orientation. The local examiners are key.