You've already been pointed to my previous post. But one thing I would expand on is that the dynamics of the question are themselves shaped by the role of Christianity in the development of Western society. Not to put this on you, OP, but this seems like a good post to talk about this issue.

Our whole concept of 'religion' as a combination of cultic activity and a world view embracing how the world is, the existence or not of supernatural entities, and personal morality and ethics, did not exist in the Roman cultural sphere. For the Romans, 'religion' in our sense was not a thing. religio refered to cultic activity and was primarily the domain of priests, that's what priests did - they performed whatever rites and rituals you needed to do to keep whatever deities were around happy, or at least appeased. Failing to do that, on a national, city, town, or personal level, was basically going to end badly because gods were reflections of human beings in that they had personalities, likes and dislikes, and a lot more power. So pissing them off was a bad idea and it was best to do religio for the sake of peace and prosperity.

This had nothing to do with view of the world or morality, which was what philosophy was for. That was the domain of groups like the Stoics, Epicureans, Platonists, etc.. They were interested in answering questions about existence, the nature of god/gods, how one ought to live one's life. This was, for most people, an entirely separate domain that had little to do with religion, except that most philosophical schools gave some kind of metaphysical explanation of deities. It is interesting to note that although philosophical schools and teachers often gave radically alternative interpretations of 'what' the gods were, none of them were particularly 'atheist' in the modern Western sense nor advocated abandoning the practice of religio. Despite repeated questions about it, it's very difficult to identify anyone in Antiquity as a 'modern atheist' and it's pointless to ask whether ancient Romans 'believed' in their religious practices. They weren't a credal matter, they weren't articles of faith. Sure, some people believed in them more than others, but this is more like being more or less superstitious, rather than religious belief. Indeed, the line between religio and superstition is far more blurred than we usually think.

All of which makes the 'competitive environment' into which Christanity enters quite different. It's not 'Christianity vs. a bunch of other religions', it's the case that Christianity combined in a relatively unique way (Judaism does the same, which is where it comes from) (a) view of the universe, (b) personal morality, (c) 'cultic' activity.

This is one reason Christianity did not 'integrate' well - unlike incorporating a new deity, or the mystery religions which functioned within Graeco-Roman polytheism and rarely approached exclusivism on a philosophical level, Christianity was an alternative to both Roman religio and Roman mores + philosophy. To convert (pre-Constantine) was a risky and decisive thing to do that essentially marked the fact that you saw the universe in a whole new way and were going to abandon Roman religio, which in the eyes of your fellow Romans was basically saying, "I don't care if your gods bring down divine vengeance on our town for not following their rules, p.s. I think they're demons anyway."

The idea of religion in the modern sense emerges from the dominance of Christianity in the Empire and the subsequent influence of this 'package' on later Western culture and society, but it is important not to anachronistically read this back into Roman religious practices.

Not to discourage further discussion, but you may be interested in this previous post by /u/talondearg that charts the early history of the Church.