I shoot my hunting bow with a loaded quiver on once a year, just to prove that I hit exactly the same out to 50 yards. If you allow your quiver to cant your bow, it would change your point of impact.

When hunting from a treestand, I always take my quiver off as soon as I get my safety belt on. For me, it is one less thing to get in the way when shooting.

It probably just boils down to a personal preference, as I am sure many deer have met their demise from a bow carrying a quiver.