Should we forgive? To take to the high road above our opponent and forgive them. You are such a good person, aren't you? Did you forgive because you genuinely believe such a person has fully redeemed themselves or did you forgive to position yourself as a "better person"? To perceive yourself as this "better person" is utterly narcissistic, letting yourself be absorbed by your superego or ideal self. You didn't forgive; you decided to ignore.
Moreover, choosing to ignore and to forgive are inherently different. If a person stole from you like a 5-dollar bill, you probably wouldn't call the cops; however, if you saw the same person again, you would probably hold your money tighter. Notwithstanding, if the person later came up and handed you back the 5 dollars and apologized profusely, swearing never to steal again, then that would be forgiveness.
To ignore is easy and makes you feel all special inside because you are such a boy scout and did the "right thing." However, forgiveness is complex and challenging. It takes change, a change for the other party to accept they did wrong, then correct their action, then it takes acceptance on your part. Acceptance that the old them is dead and arises from the ashes is a relationship from the new, to forget everything.
If these conditions are not met, it's not forgiveness; ignorance.