When emporer Constantine converted to Christianity and later when Emperor Theodosius I made it the Empire's official religion, was there an acceptance and understanding of its abrahamic oragins? Looking at earlier parts of the roman's empire history there had always seemed to be mistrust and conflict between Rome and Judea, was Christianity seen as a separate religion or was its earlier Jewish connections understood in Rome?
Initally, even during the time of Vespasian, there were Roman converts to Christianity, mostly among the poor, from the simple fact that early Christians took care of the poor, while Pagan Romans usually looked at them with disdain. In essence, Early Christianity was similar to an early form of Communism, in which the poor converts teetering on the edge of starvation had nothing to lose, and Jesus at least offered an alternative to starving to death on the street.
Later, during Constantine's and Theodosius' time, a large part of the Empire was still Pagan. A lot of people were resistant to change to a new religion, and a lot of Pagans from either social class didn't want to leave the traditions of their ancestors behind because of the Emperor's orders. This change also featured a paradox: "If the Emperor was not a deity, because God was the only deity, then why should I change my religion simply because of an Imperial command? He is not a god afterall. If God wants me to follow Jesus' teachings, why does he still allow me to worship other gods?"
There was also a historical difference even back in the 1st century, shortly after Jesus' crucifixion on how "Jewish" should the Christian religion be. There were those who thought that Christianity should be a religion only for those who were of Jewish descent and accepted Jesus as the Messiah, and those who thought that Christianity is a universal religion for all of mankind.