Theism vs. Atheism ... will it ever be settled?

You make people stop believing by offering something more attractive in replacement (and is some cases, more attractive than death by burning). The early christian church did this by adopting the pagan feast-days and merging into the indigenous culture rather than trying to supplant it - this meant that the locals weren't losing anything by adopting the new religion - they could still celebrate Beltaine, Shamhain and Saturnalia and have a big party - it was just called Easter, Harvest Festival and Christmas - and they were given Sunday's off as well - win-win. The other "incentive" that christianity offered that the pagan religions didn't was that they were more "modern" and "progressive" and centered around humanity rather than spirituality and otherworldliness. Essentially, christianity to early medieval people was hip and with-it.

 

To gain insight into how christianity endured the Roman persecutions you have to first ask why the Romans were persecuting them in the first place - this wasn't standard procedure for Roman Empire - they normally assimilated others' religions into their own pantheon of gods, and where they couldn't, such as with the Jewish faith, they granted it special status and allowed them to continue unmolested as long as they paid tax. In the beginning christianity was just a faction of the Jewish religion, they saw it as an internal "problem" of the Jewish nation and of no concern to them. So for the most part they tolerated the early christians (Nero instigated the first round of persecutions but that was because the early christians in Rome were rebellious, not because he disapproved of their religion; Roman persecutions were not continuous and relentless during this period) and continued like that, with only sporadic outbreaks of small-scale localised persecutions, for the next 250 years. This was a crucial time for the new religion as it was when the christianity grew and spread more or less unchecked. It was during this period that christianity separated from the jewish faith and the early church fathers formulated what the religion would actually be and how the church would govern it - they were allowed considerable freedom and latitude within the Roman Empire to do this and it certainly wouldn't have happened under constant persecution.

 

The persecutions of the later period were caused by many reasons - the Romans now saw the the more organised and growing church as a threat - they were seen as sectarian, separatist, secretive, atheistic (a polytheistic view of monotheism), non-materialistic and disloyal - the normal Roman procedure with new religions was assimilation, but the jews and later the chistians were having none of that malarkey. None of these features fitted with the democratic and social nature of Roman life so the christians remained "foreign" outsiders. The church endured because it adapted and what didn't defeat it made it stronger, it had seen that the Romans feared what the church represented and they drew strength from that. Ironically that resulted in producing a religion that became more attractive to an emperor who wanted to control a vast population and the persecutions created martyrs, who became saints, and those saints made the religion appealing to those use to a polytheistic religion.

 

No, the afterlife wasn't exclusive to christianity, and it certainly wasn't central to the jewish faith, but it was (apparently) a key part of many religions. Burial rituals, which are common to most civilisations in one form or another and (if the archaeology is correct) to Neanderthals too, suggest that to many religions and cultures burial is more than just mourning the passing of dead, it is preparing them for life after death and their journey to the ancestors - viking ship burials, Celtic burial mounds, Egyptian tombs, etc. etc. all suggest this is the case. Whether that was central to the religion is another matter - burial tombs survive as evidence because they were designed to - no one gets buried in a tent simply because it won't last and no one wants that. We see the Egyptian religions as being cults of the dead because the tombs are all that survive - the day to day, hedonistic, life is for living stuff is long gone.