Before we tackle the problem of harmonizing Jesus’ words on remarriage with Moses’, we need to realize there is one more biblical author who agrees with Moses, and his name is Paul the apostle. Paul clearly wrote that remarriage for those divorced is not a sin, agreeing with what the Old Testament says:
Now concerning virgins I have no command of the Lord, but I give an opinion as one who by the mercy of the Lord is trustworthy. I think then that this is good in view of the present distress, that it is good for a man to remain as he is. Are you bound to a wife? Do not seek to be released. Are you released from a wife? Do not seek a wife. But if you should marry, you have not sinned ; and if a virgin should marry, she has not sinned. Yet such will have trouble in this life, and I am trying to spare you (1 Cor. 7:25-28, emphasis added).
There is no doubt that Paul was addressing divorced people in this passage. He advised the married, the never-married, and the divorced to remain in their current state because of the persecution that Christians were suffering at that time. However, Paul clearly stated that divorced people and virgins would not sin if they married.
Note that Paul didn’t qualify the lawfulness of remarriage of divorced persons. He didn’t say remarriage was only permitted if the divorced person shared no blame in his previous divorce. (And what person is qualified to judge such a thing as that other than God?) He didn’t say remarriage was only permitted for those who had been divorced prior to their salvation. No, he simply stated that remarriage is not a sin for divorced persons.