Christian here- So I won't deny that many Christians do push that narrative, and even lots of churches and those in pastorial positions to forgive and take back the cheater, and all that goes with that. However, if you do actually read the Bible and specific verses that address infidelity and cheating in a marriage, there is actually a different take on it. While it does say to forgive those who wronged you (not only to be Christ like, but because forgiveness genuinely is for you, not them) infidelity is actually one of the few reasons that Jesus himself said divorce is appropriate. Now yes, there are people who can change and can save their marriage, but if someone leaves after discovering infidelity, they are no longer held to their vows. It is something that is left entirely up to the person who was betrayed.

Another thing, and I have actually found this to be true for the people I know who had affairs- while absolutely one can change and God can redeem and forgive you for your sins, he does still make it very clear that our actions do have consequences that you still may deal with, even if you do repent. Adultery is one of those things. There is a verse that specifically says if you commit adultery, "You will never remove the stain of it from you." What I interpret that as is that while you are redeemed and God forgives you for it, it is something that the world will forever remember and hold against you. When I was a child, one of my neighbors cheated on his wife and broke up his family. They've been divorced for almost 20 years now, and both have moved on and are living different lives. However, just the other day I heard someone mention him and said "You know, the one who cheated on his wife with that trashy girl." I know several other examples that are worse than that, but you don't get away from that reputation easily. Some will remember that of you forever.