I'm just beginning to really study these different sects of Christianity. I know that with the Donatists that when they were over run by the Saracens their churches were destroyed and many fled north. In the east when were the EO abandoned by the RCs to the muslims?
Despite the recent schism, when Emperor Comnenus called us to save Byzantium from the Muslim we fought four crusades to help the East. Some abandoning.