Merriam-Webster defines the word iconoclast (coined in 1641) as
1. a person who destroys religious images or opposes their veneration
2. a person who attacks settled beliefs or institutions
My definition of a dodecophonoclast is a person who opposes the veneration of 12-tone music. An alternate spelling would be dodecophoniclast.
Let's see if it catches on!
UPDATE: Gary Bachlund has set this blog post, and quite appropriately so, to music!