I want to use a bucket of filtered water for showering. The bucket when full weighs 20 lbs. Would hanging this bucket on my shower head pipe which is coming out of the wall damage the piping?
My mom used to bring well water back from the lakehouse for rinsing her hair; installed a shelf for those blue 5 gallon water jugs, which weigh ~40 pounds.
It seems you have a 2.5 gallon bucket, with a handle that will put the weight out at least a few inches (more like half a foot, plus). I would not do this. Perhaps a hook in the ceiling or on the wall?
If you do break it, you're looking at tearing open the wall.
It is hard to say without opening the wall you may have a metal pipe coming out of the wall and PVC or CPVC, copper or Galvanized pipe. With galvanized pipe it might be strong enough if the pipe is strapped to a stud but you would be taking a chance.