If my opponent sends Wave-Motion Cannon to the graveyard to inflict damage to me, can I respond to the damage (before it hit me) to nullify the damage via cards like Rainbow Life or Hallowed Life Barrier (i.e. cards that can be activated to manipulate damage you'd take)?

I know you can't destroy WMC to it's effect via spell destruction/counter traps; but I want to know if you can stop the lifepoint loss.

Yes, you can activate Rainbow Life/Hallowed Life Barrier to reverse/prevent the damage from Wave-Motion Cannon in response to the activation of the damage effect.

But you Cannot Barrel Behind the Door it right?

Correct.

"Barrel Behind the Door", "Trap of Board Eraser", and similar cards cannot be activated in Chain to the effect of a Continuous Spell or Trap Card that activates and will inflict damage, such as when a "Wave-Motion Cannon" or "Ominous Fortunetelling" which is already face-up has its effect activate.