You said it was a political movement that you supported. It's entirely reasonable to ask you what that movement stands for.

(Hint: The reason you're finding that a difficult question is that Anonymous is not a political movement and you're just projecting your own beliefs onto it whenever it happens to do something you think is good.)

Gene Simmons was attacked because his statements, and his position as a pop star made him a target as a threat. Like all immune systems, Anonymous is known to overreact.

If you look at the targets for Anonymous in terms of political uprisings, you'll notice a concentration of places where the internet played a large role and/or was targeted. Uprisings occur the world over, but Anonymous gets involved when the internet is threatened.

In this sense, the use of the "V for Vendetta" mask is a perfect symbol for Anonymous, for anyone who has read the comic book (or even just seen the film adaptation).

The only verdict is vengeance; a vendetta, held as a votive, not in vain, for the value and veracity of such shall one day vindicate the vigilant and the virtuous.

V was not so much interested in popular revolt, anarchism, social equality, etc. per se. He was interested in revenge. Justice became the ultimate form of revenge against a tyrannical government.

You can see that similarly in the actions of Anonymous. Democratic movements are supported against dictatorships, and transparency is supported against representatives of Democracy. Not because Anonymous is a positive force for Democracy or transparency, but because those are weapons they can wield against the internet's perceived enemies.

So yes, Anonymous is a political movement, although a leaderless, amorphous, and pluralistic one united only in negative political space. They don't seek to create, as much as destroy their political enemies. But, as some say, "the urge to destroy is also a creative urge".

...you engender such a large selection bias that I remain as convinced as ever that you're simply projecting your own beliefs onto something considerably more nihilistic. Yes, if you throw out everything that doesn't fit the quotably Bakuninian pattern you expect by saying "oh, but that was different people" or "oh, that was just an overreaction", it all becomes so clear...but if you don't, you get a messy and impure reality in which Anonymous better resembles Brownian motion than a movement.