Quite simply; iconoclasm is evil when the motivations behind it are evil.
Iconoclasm: the action of attacking or assertively rejecting cherished beliefs and institutions or established values and practices.
[I would add that the proper definition of iconoclasm is broader; and includes attacking, damaging, destroying and subverting cherished concepts, objects, symbols and rituals.]
It might be assumed that since it is 'cherished' beliefs and institutions (etc.) that are attacked by iconoclasts, then the good or evil of iconoclasm depends on the moral validity of that-which-is-cherished. It might be assumed that cherishing a good person is good, and an evil person is evil. But that is wrong and false.
What matters is the motivation of the iconoclast. When the iconoclast's motivation is evil, then it does not matter at all what is being attacked - because all such iconoclasm is evil.
And successful evil iconoclasm, when the evil-motivated iconoclast successfully destroys anything; feeds the evil of the iconoclasm by gratifying the evil motivation.
That's all we need to know.
When iconoclasts are motivated by evil, they are morally wrong in their attacks - and it does not matter a jot what specifically they are attacking.