Parodies should be affectionate tributes to the original, and should in its' own way add to the original. If they mock and/or denigrate the original they are not parodies but an ego trip for the writer, and by association the subsequent singer/s.
If someone walks out when a parody of something he has just performed is sung, then either the person singing the parody did not introduce his song properly, or the parody in question is a poor one.
There are many parodies, but there are only a few good parodies.
Another school of thought proposes, that only people who can't think up something original of their own, write parodies of the works of others.
Giok.