Why can a broken vow to God be forgiven but remarriage remains adultery?

Answer:

All sins that are repented of can be forgiven. Some don't receive forgiveness because they refuse to repent (Hebrews 12:15-17).

Breaking a promise is a sin because it is a form of lying. For instance, in the Old Law it is stated, "Or if a person swears thoughtlessly with his lips to do evil or to do good, in whatever matter a man may speak thoughtlessly with an oath, and it is hidden from him, and then he comes to know it, he will be guilty in one of these. So it shall be when he becomes guilty in one of these, that he shall confess that in which he has sinned" (Leviticus 5:4-5). Sinning against God is a graver offense, but it is still forgivable when a person repents of his sins.

Marriage vows are a part of a covenant. Covenants are lifetime promises between two parties. Because God oversees these vows, only God can set the terms for ending a covenant. As Jesus state, when two people marry, "they are no longer two, but one flesh. What therefore God has joined together, let no man separate" (Matthew 19:6).

Can broken marriage vows be forgiven? Yes, but it has requirements: "if she does leave, she must remain unmarried, or else be reconciled to her husband" (I Corinthians 7:11). A married person who goes off and has sex with another person is committing adultery. Just because they broke their vows,  it does mean the covenant no longer exists. A person who remarries without a right to remarry shows a lack of repentance for his sin. If he remarries, he is remaining in adultery. The only way to gain forgiveness is to cease sinning and changing your attitude toward sin. A thief can't say that because he is already stealing, he should be forgiven while he continues to steal. In the same way, an adulterer cannot say he should be forgiven for adultery while he continues to commit adultery.