Some just want to change, other may not have faction to join their desired deity. Here is an idea how a change of deity could work.
If you want to change deity, you go hail the new deity NPC in SoS, and you will get an option to forfit your old deity, and join with this one.
In order to forfit the old deity, you need to hand in a completed deity aug + 10.000 platinium.
If you don't have a completed deity aug (your current deity doesn't have an aug, or you don't even have a deity at all, but can't join this deity cause of faction), well you will have to go pariah, get the final aug, turn it in + 10.000 platinium, and congrats, you have now joined with your deity of choice.
If you want to change deity, you go hail the new deity NPC in SoS, and you will get an option to forfit your old deity, and join with this one.
In order to forfit the old deity, you need to hand in a completed deity aug + 10.000 platinium.
If you don't have a completed deity aug (your current deity doesn't have an aug, or you don't even have a deity at all, but can't join this deity cause of faction), well you will have to go pariah, get the final aug, turn it in + 10.000 platinium, and congrats, you have now joined with your deity of choice.