I know for example that the Romans allowed some freedom of religion in conquered territories as long as the people started worshipping Roman gods, and even absorbed some foreign gods, like the Egyptian goddess Isis, into their own beliefs. But how did they handle gods with similar spheres of influence, like Ra and Helios, or things like conflicting creation myths? Did they just assume other cultures were wrong but let them do their own thing anyway or did they have some kind of explanation?
Good question!
Spiritual and religious beliefs are complex, and there are many different ways in which individuals interpret different belief systems and ideas. One of the most influential of these was the process of interpretation graeca (or interpretatio romana).
This is used to refer to a phenomenon where Greeks and Romans interpreted foreign gods and myths through the lens of the ones they already knew. For example, a Roman might associate the harvest goddess Ceres with the Greek Demeter or the Egyptian Isis. A Greek might conflate Osiris, the Egyptian god of rebirth with Dionysius, who died and was reborn in some myths.
The reason this was possible was because neither the Greeks nor the Romans had a single “belief system”. There was no Roman Bible, and no canon of “true gods” versus “false gods”. Neither was there any one correct way to worship them, or even a requirement that anyone worship particular gods over other ones.
If you look at even Roman mythology, you will find countless variations and versions of staple myths. Many of these will conflict with other versions, sometimes wildly. And yet, this did not cause ancient people any concern. It was understood and accepted that the myths and oral histories passed down in one location would not be the same as those passed down in another. When we look at ancient religions through the lens of modern ones that require faith in core canonical beliefs, like 21st Century Christianity, we needlessly complicate things.
People living in Memphis would tell a different story about the gods than someone in Athens. But someone in say, Sparta or Arcadia, might also differ in the mythological traditions they learned. Beliefs, myths and rituals were localized and sometimes very personal.
The importance of local gods, or local versions of gods, was paramount. The most popular or important deity in one city, would be different than the next one over, and that was as things should be. In fact, it was not unheard of for the depiction and role of a god in one city to be radically different from their role in another.
People in the ancient Mediterranean were above all else pragmatic in their approach to the gods. They generally did not offer prayers or offerings to a god because they were “the best”, or “the true god” or anything else like that. They made offerings to a god to thank them for something they did, or to entice them to do something they haven’t yet.
If you were in a foreign land, it made sense to pay homage to their gods since they would be well suited to help you there. Sometimes foreign gods were worshipped within cities like Rome and Athens, including the cult of Isis (which you mention), or the cults of Mithras or Cybele.