The "Jesus was a fabrication of the Romans" thing is pretty silly (though the Gospel accounts that have come down to us, particularly Luke, show some influences of Greek culture).
That said, the fact is that the Romans tended to tolerate local religions and customs as long as the subjects kept quiet and paid their taxes.
Addendum: The Jews (and later, the Christians) occasionally had difficulties with the Roman authorities because the latter considered the trappings of the Imperial rite to be part and parcel of loyalty to the Roman state, while the former considered it to be idolatry. The situation was not unlike that of Jehovah's Witnesses who object to the pledge to the flag on similar grounds.