Whenever I try to cut out a circular hole in either a cylinder or sphere the polygons around the circular hole always have distorted normals after smoothing. Is there anyway to fix this. I've tried using the remesh modifier but wind up with some pretty ugly results.
LoopTools via menu Edit → Preferences → Add-ons → LoopTools:
In Edit Mode, press 3 to switch to Face Select mode and select a square area of faces where you want the circle to be. Click RMB > LoopTools > Circle. Make sure you uncheck Flatten in the
Adjust Last Operation panel that appears in the lower left corner to avoid distortions on the curvature of the cylinder. I recommended to inset with i and to add edge loops.