Would the supporter of one Presidential candidate, who publicly referred to another Presidential candidate's religion as a 'cult', be considered an iconoclast?
My take is no. To be a breaker of icons, the icons need to be generally accepted. A Mormon who speaks against basic Mormon teachings would be an iconoclast, as would a Catholic who goes against the Pope's rule. If one doesn't accept the "word" of a religion, they are not necessarily an iconoclast, just a non-believer. I believe you have to have been part of something, or that the something is so endemic to your society that being against it is seen as wrong, to become an iconoclast.
I may be wrong, so pile on folks and let us know what you think it takes to be an iconoclast.