I agree, James. If the Christians had just come along and said "Hey, this is our god and this guy Jesus, was his son and this is sort of how it went down..." the Romans probably would have said, "Oh. Sort of like Hercules, huh? Okay, bit weird, but okay." Once they started saying their god was the One and Only God and that all the Roman gods were false/evil/demons, the Romans started the unpleasantries with them.
If that had been how it went, I don't think any of the polytheistic traditions around at the time would have had any problems with the Christians. Just another god fathering a mortal son who did some great stuff. Nice stories, but nothing that unusual. Jove did it all the time!