What is the reason for the non-acceptance and non-elevation of the deeds of quarreling Muslims, and what is the divine wisdom behind this? Is a verbal greeting without a handshake sufficient to avoid this ruling?

Allah is not questioned about what He does, but they will be questioned. The Prophet, peace and blessings be upon him, informed us that the deeds of disputing parties are not presented to Allah until they reconcile. This is because Islam encourages brotherhood and affection and forbids turning away from one another and cutting ties. Due to the grave sin of animosity, enmity, and rancor among believers, sins between people are forgiven when they reconcile and forgive each other. Breaking off estrangement occurs by offering greetings, and shaking hands is not a condition, though it is preferable.