The Greeks and Romans were doing it long before Alexander, as were all the cultures of the Mediterranean and Ancient Near East as far back as history allows. Egyptians were borrowing Levantine gods early in the Bronze Age, and ancient Akkadian adopted the Sumerian pantheon wholesale.

Turns out, culture isn't a singular thing you can just have. People everywhere all the time are picking up bits of things to do, things to say, things to believe in, and borders, no matter how fluid they are, only exist in the aggregate.