Part 15: Sleep of Bronze discusses why sacrifices were no biggie.

There were plenty of pagan/Hellenistic mystery cults that promised pleasant afterlives, and sacrifices were very rarely a burden on a household, because you happily ate it afterward. (The sacrifices certainly weren't human either, as you might have guessed by the eating part.) Pagan worship was probably less onerous than early Christianity, for that matter. Many more festivals, and much more communal and civic, compared to the more personal aspect of Christianity.

My area is very much not Christianity so this is a fairly uninformed approach, but I've never seen or been convinced of anything inherent to Christianity that allowed its rise, save that it commanded it be spread, that it be preached. It was an active, proselytising religion, surrounded by faiths that were instead handed down by tradition: faiths that had cheerfully met each other, shared a few gods, and continued on; faiths that barely understood external opponents at all. It was a problem they had very little context for.

Then, eventually, Christianity managed to get its hooks in some senior officials like Constantine, was lucky enough to be on the winning side on a couple of occasions, proved useful politically, and organised paganism was doomed pretty shortly after. (Unofficial paganism, particularly of the rural sort that stuck Jesus' name on old traditions and did very little else, continued for many many centuries into the future). Julian did his best to open things back up but didn't really stand a chance.