"Have we not all one Father? Did not God create us? Why do we profane the covenant of our fathers by breaking faith with one another? Judah has broken faith. A detestable thing has been committed in Israel and in Jerusalem: Judah has desecrated the sanctuary the Lord loves, by marrying the daughter of a foreign god." NIV translation
Now the focus shifts from the priests to the people and their unfaithfulness. The questions are asked to get the people to understand what has happened in that they have turned their backs on their own people (God's people the Jews). They have broken faith by marrying a non-Jewish woman. This marriage is described as detestable and even a desecration of the sanctuary. If the sanctuary was desecrated (made unclean) then it could not be used for worship (sacrifices) and sins could not be atoned for until it was purified.
"As for the man who does this, whoever he may be, may the Lord cut him off from the tents of Jacob - even though he brings offerings to the Lord Almighty." NIV translation
In verses 10 & 11, the effects of this sin were described and we saw that they affected the entire nation of God's people by desecrating the temple. Here, we see what God says to do with the individual and that is to remove him from the fellowship with the rest of God's people. Even if he brings offerings, he is to be removed because he is still with the woman that God said not to marry. There is no repentance so there will not be forgiveness and the sin will continue to affect the body like a cancer unless the cancer is removed.
"Another thing you do: You flood the Lord's altar with tears. You weep and wail because he no longer pays attention to your offerings or accepts them with pleasure from your hands. You ask. 'Why?' It is because the Lord is acting as a witness between you and the wife of your youth, because you have broken faith with her, though she is your partner, the wife of your marriage covenant." NIV translation
This passage is an example of trying to get forgiveness without repenting of the sin. It speaks of how the people went to the altar with sacrifices and tears but did not want to change their practices (repent). They are trying to have both worlds - the one in God's will with the women He has chosen and this world where the men chose women that God said not to marry. They are trying to get God to ignore their sin but God is simply letting them know that, by not making a choice, they have really made the wrong choice. That same choice is ours today in every aspect of our lives. We can choose to listen to God, through His Word and the Spirit, and do as He says or we can do things our own way but we cannot get God to ignore our disobedience.