This thing happened a few years ago at anonymous' first big meet and scientology has a history of harassing and ruining the lives of people that go against them. Therefore I do not feel that anonymous is in the wrong in this instance and I think scientology should stop being weird and creepy.
A religious group should be able to go about their day and practice their religion in peace. This is true as long as the group isn't hurting anyone. It's not appropriate for Anonymous to spam the Church of Scientology in a way that costs them money. This is intended to interrupt their freedom of religion.
That's an old trick. Originally, the tactic was used against companies that were junk faxing other companies with advertising and sales pitches, early spam. Annoyed recipients would create a few all black pages, load them into a fax machine, tape them together into a loop so the faxing would be continuous and endless, and fax the spammers in retaliation. The companies doing the junk faxing didn't much like that. Forgot to mention, the objective wasn't to deplete ink cartridges, rather, it was to use up paper. This was when fax machines used thermal paper, so there wasn't ink to be used up. However, the thermal paper was a lot more expensive than the ordinary paper that's used today. I remember thinking it hilarious and laughing when reading articles describing how people at the junk faxing companies would come in and be really dismayed to see the floor littered with completely black and useless expensive paper.
Although there is a little bit of humor in this prank, it didn't have any lasting effect on the church, and it only makes Anonymous look like children. There are better ways to make Scientology look bad, there's no need to resort to childish pranks that only generate internet headlines.
It is my belief that Anonymous is only wasting its time and further lowering their reputation among the general public by engaging in such frivolous activities. This incident will not significantly harm the Church of Scientology and does explain why exactly Anonymous objects to the Church of Scientology. Anonymous is simply trying to get some free publicity.