I think it depends on the framing. Do we pick certain people to keep, or is it random? Do they all just disappear and get Raptured one day, or do we have some time to prep?

I'd guess that we could probably get by with a few million without a massive drop in quality of life, but that's if we had time to prepare. Wiping out 99.99% of the human population all at once would not result in a good time for the survivors.