Generally, the pantheons stay separated. Even my own Greek and Roman aspects functioned as separate entities for quite some time. Though if a divine being makes a habit of walking the Earth in mortal guise, they're bound to bump into a foreign god eventually. That's generally how I encounter other deities.
Though the Abrahamic Celestials and other beings from that pantheon tend to keep to themselves.
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Though the Abrahamic Celestials and other beings from that pantheon tend to keep to themselves.