If I'm expecting to bowhunt in rain, I use my Catquiver. However I have been caught out there with my backquiver.
First, I always carry a hood to protect the feathers even though I silicone them prior to any hunts. If your backquiver rides properly on your back, it's mostly off to one side so very little if any rain should be a problem.
When I'm in my natural blind or just hiding, I lay the quiver flat on the ground during any rain. Again, don't really see this a problem.
Quiver should lay on your back very similar to this photo