The empire split after Alexander's death into the Macedonians proper, the Seleucids in Asia, and the Ptolemies in Egypt. The Ptolemies certainly kept a lot of cultural continuity with the Greek / Macedonian world -- so much so that the last Ptolemaic pharaoh, Cleopatra, is believed to have been the first one who was able to speak the Egyptian language (after ruling Egypt for 250 years!). They did set up syncretistic temples, which was standard practice basically everywhere in the classical period. That was an effort to get the Egyptians to accept Greek religion, not the other way around. The Ptolemies even set up a major new city for Greeks. Their accommodations to Egypt weren't particularly impressive.
To the extent that the Greeks and the Macedonians had a common cultural identity, it was because the Macedonians aspired to Greek culture (it seems safe to say that the Ptolemies eventually succeeded at this). The Greeks didn't think highly of the barbarians to their north.