The big rip would imply that eventually, all points in space are accelerating away from one another faster than the speed of light, which would tear apart atoms

The big rip would imply that eventually, all points in space are accelerating away from one another faster than the speed of light, which would tear apart atoms, subatomic particles, and everything down to the smallest divisible units of matter and energy. The accelerating expansion doesn't imply this at all, and would instead leave big dense things like galaxies intact to burn out and fade away. Acceleration comes from the cosmological constant - more volume means more dark energy, which means more velocity (acceleration). Only if the cosmological constant isn't constant would we expect a big rip. Now, we're questioning the acceleration part also apparently.