For example, if a man's wife cheats on him, they divorce, and she remarries later, is there a Biblical basis for him being indifferent to her once she apologizes?
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Do not make everything into a "law." There are principles of truth, such as loving ones neighbor or brother as yourself, but it also requires trust to maintain a transparent relationship, any relationship. Once trust is broken it is more the duty of the offender to prove his/ her trust.
I'm thinking of the sinful brother in the Corinthian church who was put-out until true remorse was seen by him changing his life. Restoration is always the goal, but so is moral change—integrity. The rest is between you, God and that person.
Love always has actions. Do you think that indifference is an attribute of God's love? My wife divorced me 20 years ago and, lied about me and married a close friend of ours. I went through many stages of grief and anger, mostly because of the suffering of my children. It was only about a year ago that the Spirit made me realize that I, of all people, would be her access to God's restoration and forgiveness, and I then gave myself to the desire to pray for her and treat her as though nothing had ever come between us; also as if we had never been married. My life is totally disconnected to our past; no guilt, no resentment, total forgiveness; no longer waiting for her to repent, but releasing her so she can repent; loosing her from her own fear and guilt. My goal is to see the family come into spiritual unity. This only implies that there will be peace, not that we will every have an intimate relationship again. It is working. God is working.