A religious organization once asked me to speak to an audience of priests about the persecution of the early church. I began by saying 'If we were in ancient Rome, the authorities would throw the lot of you to the lions - and the authorities would be right.'
Classical religion was a civic affair. That's why priests were politicians. Basically, the city - or state - adopted a particular god as a protector and sacrificed and performed ritual celebrating that god in return for blessings and protection. This was an explicit pact summarized by the expression 'Do ut des' (I give in order that you give).
This had nothing to do with belief, and absolutely nothing to do with private beliefs. People in an ancient city no more had to believe in their god than I have to believe in Revenue Canada. However, if either of these two entities do not get what they consider as their dues, they tend to get dangerously irritated. However, while the wrath of the taxman falls on my head alone, the wrath of the god fell on an entire community.
So, from an ancient point of view, what Christians got up to at home or among friends was their business. However, refusing to attend sacrifices and rituals, and even standing on the temple steps preaching against the god was the social equivalent of lighting cigarettes in a firework factory and insisting it is your right to smoke. In short, you have become a public menace.
Once Christians had reached a certain percentage of the population it seemed to the Romans that the gods did indeed withdraw their protection in response to Christian disrespect. That was the cue for barbarian invasions, earthquakes and plague. As we know, correlation is not causation, but someone who has just buried his family in the smoldering remains of his home might not have regarded matters so dispassionately.