If someone does something wrong and then afterwards they see the error of their ways forgiveness should be automatic. If they genuinely think what they did is wrong they will feel ill will towards themselves. You don't need to feel ill will towards them, they've changed, they're no longer the same person.
It doesn't mean they have to be let off, doesn't mean they shouldn't be punished or have to make reparations. But the "hate" so to speak is targeted at what they were, not what they are and so it becomes redundant. Now of course you can't know if they are genuine, you can't see inside their heads. Only they can know that.
So in a sense forgiveness is meaningless. If someone is part of your life, then they may have the opportunity over time to prove that they are genuine. If they aren't part of your life, well I suppose forgiveness would help give them a chance to prove to themselves that they are genuine.
Ultimately, you don't need to maintain contact with them but you should try to accept the apology. You should do this for your own sake. It's about you, it's about what kind of person you are. If it's difficult that fine, you don't have to, you don't need to torture yourself or feel guilty or anything. But you should always strive to be the best person you can be, you should try to do what's right even when things are difficult. Not responding won't reflect badly on you, but responding positively will be a clear display to yourself of your good character.