The extenuating circumstance of having become evil under the influence of the Dark Lord provides a much weaker reason to rescue someone, and requires much more trust in the person who is conveying the information (since they must not only get the facts right, but make some subtle and complex judgments about the prisoner's character and what they deserve).
If Harry is a utilitarian, he shouldn't need extenuating circumstances. He should want to free everyone from Azkaban and from all forms of torture and suffering, including truly evil people. The only reason not to free Bellatrix Black should be the danger of her attacking other people later on, and that's the point on which he should seek reassurance from Quirrel (re: what they are going to do with her once freed).
But it seems Harry reverts to common human morals in the last few chapters. He attaches much weight to Bella's innocence. He thinks he'd like to kill Voldemoret as revenge or punishment.
There's also the TDT idea that people who did evil things should be punished.
[Update: and now there's a fifth discussion thread, which you should probably use in preference to this one. Later update: and a sixth -- in the discussion section, which is where these threads are living for now on. Also: tag for HP threads in the main section, and tag for HP threads in the discussion section.]
The third discussion thread is above 500 comments now, just like the others, so it's time for a new one. Predecessors: one, two, three. For anyone who's been on Mars and doesn't know what this is about: it's Eliezer's remarkable Harry Potter fanfic.
Spoiler warning and helpful suggestion (copied from those in the earlier threads):
Spoiler Warning: this thread contains unrot13'd spoilers for Harry Potter and the Methods of Rationality up to the current chapter and for the original Harry Potter series. Please continue to use rot13 for spoilers to other works of fiction, or if you have insider knowledge of future chapters of Harry Potter and the Methods of Rationality.
A suggestion: mention at the top of your comment which chapter you're commenting on, or what chapter you're up to, so that people can understand the context of your comment even after more chapters have been posted. This can also help people avoid reading spoilers for a new chapter before they realize that there is a new chapter.