It is my understanding that the pharaoh was a religious ruler and the majority of the Egyptian people believed in the Egyptian gods. So how did that work under the Ptolemaic dynasty?
Polytheism in Greco-Egyptian cities such as Alexander shows that there was a high degree of syncretism between Hellenic and Kemetic beliefs and Gods under the Ptolemaic dynasty, such as the promotion of the God Serapis and other including Osirus-Dionysus and Hermanubis.
So while the Egyptian and Greek had different pantheon and religious practices there is no great evidence of religious intolerance or oppression of the Egyptian under Greek rule, on the contrary, the Ptolemies utilised the Egyptian Pharaonic institution to its full effectiveness as a political instrument - the fact that the Ptolemies accepted their deification by the Egyptian people contributed to the tensions between the successors of Alexander since while in Greece postmortem deification was acceptable, the same cannot be said of the deification of living.
there is a subreddit that deals specifically with the religion of the Ptolemaic era which may have answers to any other more detailed questions.