
John G. answered 08/15/19
Flexible tutor with MA in Classics
Non-abrahamic religions, or what we would refer to as "pagan" religions, were not thought of in the same way as modern religions are. Modern religions focus on systems of beliefs and structures that require both believing in certain things and following organized structural heirarchies in order to be considered a "member" of that religious faith community. Membership in one, furthermore, necessitated not being a member in any other.
Ancient religion did not work that way, and were instead a large conglomeration of overlapping cults and religious practices. While many of these groupings often went together - those who participated in festivals to Zeus would also be likely to participate in Bacchic cults and sacrifice to Athena, but not participate in the mysteries of Osiris; this is not a hard rule, however, and we do find many instances where people would worship gods that were initially both Greek and Egyptian in origin. When cultural contact happened long enough, in fact, gods would often "merge;" for example, Alexander the Great called himself a son of Zeus-Amun, showing that the Greeks did not even necessarily view the gods of different cultures as different gods, but rather the same gods with different names.
So, to answer the question in short, it would depend upon the person. Some might worship Zeus/Jupiter; others might participate in the mysteries of Osiris or worship the sun god Amun-Ra. Some might even do both.