It is VERY important to cut clothing fabric on grain, and pulling threads is the easiest way to accomplish that. If the pieces are cut with the grain running wrong the garment will not hang right, and if any directional elements are present it won't look right either.
I have done it with quilting fabric that was really off grain, but not often. The pieces we use for quilting don't have to "hang", and they are smaller. We can fussy cut if we're concerned about matching stripes or plaids or other design elements. And even if the grain is off a little, the cut will not be on a serious bias, so it is usually okay. When we line up the selvages, we are trying to put the fabric on grain, and that is usually enough for quilting.