Empires have always been unstable entities, prone to power struggles and internal plots as well as dissension and rebellion, and this is why emperors have long tried to unite their territories by getting people all on the same page in philosophy and religion. People who subscribe to similar ideas and worship the same god or gods tend to be easier to bring into line in other ways. Let's see how this works by looking at an example.
The biblical books of 1 and 2 Maccabees (considered apocryphal texts by some) discuss the history of the Jewish people under the rule of the Seleucid empire. Antiochus IV Epiphanes rose to power in 175 BCE and wanted to unite and stabilize his kingdom. Therefore, he issued an order that all people within his borders must abandon their traditional religious practices and customs and embrace Greek traditions. Antiochus wanted to solidify his power through this move. If everyone in the empire thought the same way, they could be controlled more easily. There would be unity among them and a stronger pressure to obey the king in all areas.
Of course, Antiochus didn't count on a strong pocket of resistance and rebellion among the Jews, led by Mattathias and his sons. These men and their families and followers refused to give up their Jewish faith and the worship of God. They rebelled, and they fought for years both against Antiochus (and his agents and successors) and against Jews who did give in to the king's orders and changed their religion and philosophy. Judaism survived and prevailed.
An exception to this practice would be the later Roman empire. After the legalization of Christianity, multiple religions and philosophies were tolerated within the empire, and people had an unusual freedom to worship and think as they saw fit.