What time period are you interested in? The distinct civilizations we think of them as were seperated by hundreds of years. Egypt was part of the nascent Roman Empire after Octavian conquered Alexandria in 30 BC, and had been under Greek control for centuries. The Ptolemies installed by Alexander after his conquests styled themselves as successors to the pharaohs. You can find depictions of them in Egyptian and Hellenistic styles, and they took on many local customs. Thus, the history of mixing traditions with their neighbors to the north of the sea was strong before the Romans arrived. This applied even to treatment of the dead. For instance, burials from Fayum are done in an Egyptian manner, but the sarcophagi feature portraits in the Roman style. This indicates a blending of traditions rather than a conflict.