Hoaxes involving fake social wrongs, be it crimes or harm to children, aren't acceptable. The way those hoaxes work is by mocking people for being caring, law-abiding citizens. That's not just taking advantage of the support of the fandom tribe, that's decreasing the likelihood of an altruistic response from society in general, and there's a reason that's not acceptable - societies survive and thrive based on displays of altruism from members. He's just decreased the likelihood that those people will respond to someone who needs help in the future, which could well result in a child who needs it not getting help - certainly that one person's contacts are likely to be unavailable in future. Even beyond a fandom perspective, that's not appropriate. It's a tremendous squandering of the resources a society has on offer to keep running smoothly and protect its vulnerable members. I'd be inclined not to forgive that one, particularly not with that poor show of understanding of the problem and the desire to cover it over rather than put it right. He did real harm to the community there.

Being offensive is less damaging to the structure of the community, in and of itself. I think that one can be overcome, provided, again, there's an understanding of what the offense was and a desire to make it right. Since I don't know the filk in question, I can't say much about that, but that is one of the better apologies I've seen lately. And good on him for disabling comments and making it straight apology, not a ping-pong table for supporters and detractors.

To be honest, fandom doesn't have a lot of punishments available except for shunning and/or the loss of reputation. What does a person have to do to regain goodwill and reputation? That's the question of the ages. But I think the minimum prerequisite for forgiveness is genuine expression of regret for the transgression and the desire to earn forgiveness.