Alexander respected Egyptian culture and religion, but he installed a Greek government to control his administration of Egypt. Greek influence in Egypt was reinforced by the settlement of Greek veterans throughout Egypt, where they became a privileged aristocracy that gradually assimilated with the Egyptians.
The question gives you a hint to the answer. If there is a president and vice president from two different political parties, it would make sense to have problems based on different beliefs, because you two don't believe in the same course of action for the country.
An executive agreement made by the president requires the approval of "no one" if it is an executive order--which is one of the things that makes the President so powerful.
