Atheist living in Spain here, I would argue to start with that adios does not mean “to god”, I would say “a dios” does mean “to god” but that “adios” just means “bye”. Perhaps the origin of the word has something to do with gods but I would argue that it meaning “to god” would not even occur to any of my Spanish friends.
Personally I dont use adios, I use “nos vemos” meaning “we’ll see each other”, but that is nothing to do with any gods, it’s just my style.
Having said that, I have no problem using the word god or gods in any language, I just dont see why anything like that should bother anyone ever.
I never say “oh my god” in English, I don’t seem to use any god related terms except for one, that being “me cago en dios” meaning “I shit on god”, something that I use when things are not going well, however it is 50–50 if I use it, some times I’ll say I shit on god, other times I’ll say I shit in the milk “me cago en la leche”.
EDIT:
I’m sure “adios” originally meant “to god”, because we also have “vaya con dios” meaning “go with god” as another form of saying bye, but in it’s modern usage, I don’t think anyone would say “adios” has anything to do with gods, just like no one would say “ventana” has anything to do with “viento” or “ventilar” (the wind/ventilate).