Deuteronomy 13 is a strong reminder that we are immersed in a very different theological context from modern Judaism or the other so-called Abrahamic religions -- Christianity and Islam. One could also include Mormonism (I know they've decided they don't like that term) and various other offshoots from the Big Three. These are all monotheistic, and the mainstream view is that they are all trying to understand and worship the same God, albeit with different rituals and different though overlapping mythology. That's why we can have interfaith councils and ecumenical prayer services. That's not to say that there aren't some true believers who condemn apostasy and attempts to convert people from their version of the faith to another. In a few Islamic countries, trying to convert people from Islam is a crime. However, that is different from what this chapter is about.
Yahweh is specific to the Hebrews. Other people have other Gods, who are just as real, though Yahweh would like us to know they are not as powerful as he is. He isn't interested in converting other people to worshiping him, and he doesn't care what gods other people follow, although he does plan to murder all the people in the land he intends to give to the Hebrews. Outside of that land, however, he doesn't care what other people do. What matters is that his people remain loyal to him. Of course, not even the most orthodox of Jews follow these commandments today, and if they did, even in Israel, they would be guilty of murder. But this is where we are in the Seventh Century BCE.
BTW NIV has "troublemakers" in verse 13. This is literally "sons of Belial," Belial being a generic name for a wicked or worthless person. It occurs many times in the Tanakh. KJV usually translates it literally, but it isn't referring to an actual family. It's kind of like saying sons of bitches.
13 [a]If a prophet, or one who foretells by dreams, appears among you and announces to you a sign or wonder, 2 and if the sign or wonder spoken of takes place, and the prophet says, “Let us follow other gods” (gods you have not known) “and let us worship them,” 3 you must not listen to the words of that prophet or dreamer. The Lord your God is testing you to find out whether you love him with all your heart and with all your soul. 4 It is the Lord your God you must follow, and him you must revere. Keep his commands and obey him; serve him and hold fast to him. 5 That prophet or dreamer must be put to death for inciting rebellion against the Lord your God, who brought you out of Egypt and redeemed you from the land of slavery. That prophet or dreamer tried to turn you from the way the Lord your God commanded you to follow. You must purge the evil from among you.
6 If your very own brother, or your son or daughter, or the wife you love, or your closest friend secretly entices you, saying, “Let us go and worship other gods” (gods that neither you nor your ancestors have known, 7 gods of the peoples around you, whether near or far, from one end of the land to the other), 8 do not yield to them or listen to them. Show them no pity. Do not spare them or shield them. 9 You must certainly put them to death. Your hand must be the first in putting them to death, and then the hands of all the people. 10 Stone them to death, because they tried to turn you away from the Lord your God, who brought you out of Egypt, out of the land of slavery. 11 Then all Israel will hear and be afraid, and no one among you will do such an evil thing again.
12 If you hear it said about one of the towns the Lord your God is giving you to live in 13 that troublemakers have arisen among you and have led the people of their town astray, saying, “Let us go and worship other gods” (gods you have not known), 14 then you must inquire, probe and investigate it thoroughly. And if it is true and it has been proved that this detestable thing has been done among you, 15 you must certainly put to the sword all who live in that town. You must destroy it completely,[b] both its people and its livestock. 16 You are to gather all the plunder of the town into the middle of the public square and completely burn the town and all its plunder as a whole burnt offering to the Lord your God. That town is to remain a ruin forever, never to be rebuilt, 17 and none of the condemned things[c] are to be found in your hands. Then the Lord will turn from his fierce anger, will show you mercy, and will have compassion on you. He will increase your numbers, as he promised on oath to your ancestors— 18 because you obey the Lord your God by keeping all his commands that I am giving you today and doing what is right in his eyes.
- Deuteronomy 13:1 In Hebrew texts 13:1-18 is numbered 13:2-19.
- Deuteronomy 13:15 The Hebrew term refers to the irrevocable giving over of things or persons to the Lord, often by totally destroying them.
- Deuteronomy 13:17 The Hebrew term refers to the irrevocable giving over of things or persons to the Lord, often by totally destroying them.