Yes and no. The vast majority are just script kiddies who want to be edgy. The real power (and drawback) of Anonymous lies in the fact that anyone can claim to be a part of it. Anyone can hack something, then attribute it to Anonymous.

The reason Anonymous doesn’t get more huge public hacks is because the people doing the hacking largely aren’t interested in giving attribution to some giant faceless organization that didn’t help with the hack. It’s sort of a catch-22, where anyone can claim to be Anonymous, but the venn diagram of “really good black hat hackers” and “people who are willing to give credit to some faceless organization that hasn’t helped them at all” is two almost entirely separate circles. The best black hat hackers largely aren’t interested in it, because they’re hacking for money or prestige, not politics.