The wonderful truth of the Gospel is that, through the atoning blood of Jesus, forgiveness and reconciliation are possible. This is a "righteousness that exceeds the righteousness of the Pharisees".
Does that mean that you MUST forgive and reconcile? Well, Jesus taught us to forgive "seventy times seven times". He went above and beyond the traditional teaching of his time. The disciples exclaimed that "this is a hard teaching". And it's true. Forgiveness and reconciliation are not for wimps or pushovers.
But forgiveness does not mean that you trust the person who harmed you. And it does not mean that you must continue to endure the abuse, shame, neglect, and sin of the other person. It means that you are willing to let go of the desire to ragefully punish the person who harmed you. You give vengeance to the One who said "Vengeance is mine". In other words, you let God be God and you acknowledge that you are also a sinner in need of grace.
All this debate about when divorce is allowed ... we're missing the point. The point is that any marriage CAN be saved and reconciled by God's grace and the gentle restoration of spiritually mature people.
Reply: I agree that reconcilliation and forgiveness should always be the first reaction of a believer, and repentance should be urged from their partner. Jesus was different from the Pharisees who said that Moses commanded us to divorce an adulterer. Jesus said divorce was only "allowed" by Moses, and only when the marriage vows were broken "hardheartedly" (an OT word meaning stubbornly unrepentant).
When someone constantly carries on breaking their marriage vows, there comes a point when forgiveness is merely condoning further sin. Eventually the wronged partner has to say: Enough is enough - this sinning must end. At that point they have to take the very difficult step of saying that they will get legal recognition that the marriage has been irreparably broken - ie they will file for divorce - if their partner does not change their behaviour.
This is always a very difficult decision and can never be decided by anyone except the person who may be suffering constant mind-numbing abuse out of the public eye. We cannot tell, outside the marriage, how much suffering is going on inside.
It is, as you say, wonderful that the blood of Jesus wipes away all sin, and that believers are given the strength to forgive and forgive. It would be wonderful if all sinning spouses repented, so that all marriages could be saved, but sometimes even those who call themselves believers carry on sinning and sinning without reprentance or without changing their ways. And sometimes divorce is the right way forward, but only the victim can decide when that point has arrived.
Even God reluctantly divorced Israel when broke her marriage vows again and again. See the details in my Divorce and Remarriage in the Church.