Did Moses worship Egyptian gods while living in the palace? When and how did Moses first learn about the true
God? Did the princess teach him about Egyptian gods or the God of Israel?
Moses' mother was hired by Pharaoh's daughter to nurse him and it is only after he is 'grown' that he was brought to Pharaoh's daughter to be her son.


And Pharaoh's daughter said unto her, Take this child away, and nurse it for me, and I will give thee thy wages. And the woman took the child, and nursed it.




And the child grew, and she brought him unto Pharaoh's daughter, and he became her son. And she called his name Moses: and she said, Because I drew him out of the water.



[Exodus 2:10 KJV]

Moses' mother could well have instructed him, first, in the Hebrew fashion before he learned anything else. Moses never mentions anything in his writing that would indicate he was ever indoctrinated into Egyptian ideology.
Doubtless as an adopted grandson of Pharaoh, Moses would have been instructed in all the ways of Egypt but he chose not to follow them, personally.
At the age of forty, when he was 'grown' as an adult he clearly aligned himself with his Hebrew heritage :


And it came to pass in those days, when Moses was grown, that he went out unto his brethren, and looked on their burdens: and he spied an Egyptian smiting an Hebrew, one of his brethren.




And he looked this way and that way, and when he saw that there was no man, he slew the Egyptian, and hid him in the sand.



[Exodus 2:11 KJV]

The writer to the Hebrews clarifies Moses' own, personal, attitude :


By faith Moses, when he was come to years, refused to be called the son of Pharaoh's daughter;




Choosing rather to suffer affliction with the people of God, than to enjoy the pleasures of sin for a season;




Esteeming the reproach of Christ greater riches than the treasures in Egypt: for he had respect unto the recompence of the reward.



[Hebrews 11: 24-26 KJV]