I don't think letting people into society who have proved themselves a danger once, and who cannot demonstrate that they have changed, is justice. The principle of "innocent until proven guilty" is about deciding whether to punish people; it's not a principle that you can reasonably apply every single day once that punishment is first carried out.

The place to determine whether someone can be released into the public is a parole hearing. That parole hearing can take into account the fact that the person in question has already been proved to be criminally dangerous. This is part of the punishment for violent crimes: once you've been proven dangerous, the presumption that you're safe is gone. Having proven that you're dangerous, it's at least somewhat incumbent on you to prove that you have reformed and are safe.

It's worth being clear about why there's a difference. Basically, most people are mostly good, and not violent. If that were not the case, "innocent until proven guilty" would not make sense - it's only because we understand from experience that we can afford the presumption of innocence that this isn't a disaster. But after someone is convicted, that heuristic changes: many more people (I won't say "most" because I don't know it for a fact) who have been convicted of a violent crime are violent, as an aspect of their character. So blindly applying the same principle doesn't make sense - it will be wrong, and result in people suffering harm, far more often.

The result is a small number of people remaining locked up who were safe to release. Just as we accept that initial convictions will occasionally be wrong and result in locking people up who never should have been though, that's the price you pay for generally trying to keep people safe.