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.