I think they are related. I will speak about my own experience. I have not seen religious Gammas some SEEs I know have religious beliefs but never obey the rules of religion.

IEIs and EIIs I have met for example, are always spiritual. SLIs also like to believe in spiritulity. IEEs and ESEs are go with the flow, will discuss with you any point of view specially the IEE, to the point I don't exactly know where they stand. SLEs and LSEs don't care much about religion, but have some beliefs. LSIs are conservative and deep down believe in religion, specially God, but might criricize some religious sayings. SEIs like to be spiritual. I have never met a religious or theist LII. ILEs debate about religion alot but are never religious themselves and don't care about it much more than IEEs.

Share you experiences and point of view please.