I've been thinking about this topic for a while, whenever someone tries to lecture me about "forgive and forget" and "giving those who learned their lesson another chance", and I think I've finally come to the right answer.
My biggest hangup has always been how do we separate those who legitimately feel bad and want to make amends for what they've done from those who keep trying to jump to the winning side as the tides change? Is there any way to tell the difference before it's too late? This shouldn't surprise anyone, but the best way to filter them out is to treat them all like the latter, at least for a while.
In both history and fiction, reformed villains who do heel-face turns spend years, decades, sometimes even THEIR ENTIRE LIVES facing scorn for what they did in the past even as they try to do the right thing going forward. However, because they legitimately feel bad for what they've done and want to repent, they continue to do the right thing despite their horrible treatment and view it as their cross to bear, this is the punishment they deserve.
Contrast that with the other group, the opportunistic backstabbers who just want to be on the winning side to save their own sorry asses. If they are not immediately given forgiveness and greeted with open arms, they cry about how unfair it is, how they learned their lesson and are still treated poorly, how we're just as bad as the other side, etc. They don't feel bad at all for what they've done, they just want to be accepted by the winning side and if they're not they immediately start causing problems.
Because of these truths, I think the best way to filter out the legitimately repentant from the bad actors is by treating them all like bad actors, at least for a while. The bad actors will eventually out themselves (most immediately, some may last a little while before giving in) and can be permanently written off and exiled. The legitimately repentant will accept their punishment, because they ACTUALLY WANT TO REPENT and will bear their crosses, they're not just in it to jump to the winning side so they can live an easier life.
So basically, don't "forgive and forget" until they've PROVEN they are actually repentant. After they've gone a few years putting up with the scorn and being treated like an enemy/outsider, and they haven't complained and continue to try to do good, THAT is when you start the process of re-integrating them and giving them another chance. If you let them off without any punishment, you're just opening yourself up to another infiltration and backstabbing by the usual bad actors.