Rome was already failing. Christianity and some guy named Peter was just the next big thing to fill the power vacuum. from what the history books and the Bible says Peter was all about being in charge and not sharing that power. oppression of women, can't talk to God unless you had a priest to do it for you, etc. just right sort of power grubber to take the reigns from Rome. biggest con job of all time. give me all your money and power and ill make sure you get into heaven. yuck. people bought into b / c life was so scrappy from the wars as Rome fell apart and all the nations it had conquered broke free.
The leaders of Rome did not like the idea of an "all powerful" being. They did not like this because the leaders wanted to have the power instead of an all powerful god. In many ways however, Christianity helped preserve the empire because it was not a self centered religion. It encouraged helping others and not being selfish. It made people do the right thing because, if they didn't, they thought they were going to go to hell. That's about all I can think of right off the top of my head because my school just got done with this so it's still pretty fresh in my brain