Dr. Martin Luther continues his commentary on Deuteronomy with this summary of chapter 13 – and it´s good reading in this translation by Richard R. Caemmerer in Luther´s Works Volume 9, pages 129-131:

To confirm what he said at the end of the preceding chapter—“You shall not add to it, etc.”—Moses now presents this whole chapter. It is his will that we adhere to the Word of God with such devotion that we are not moved by persons or signs, however learned and holy they may be, like prophets; or by brothers, sons, and friends, however good and gentle they may be; or by cities and powerful people, however great and many they may be. One must rest wholly on the Word alone and shut out everything from eyes and senses, because when the Word is lost, God is lost. It is better to lose friends, brothers, saints, mighty ones, and everything than to lose God.

When Jesus Christ commands: “Beware of false prophets!” (Mt.7,15) he gives everybody the right – no, more the duty! – to judge doctrine, spirits and prophets even…

And here you see that the right to judge the doctrines even of lawful prophets is entrusted to each person—just as Christ also commands in Matt. 7:15: “Beware of false prophets”—although no one but the government is allowed to execute outward justice and kill such a prophet, as we shall be taught in a following chapter. Each must watch over his own conscience, and therefore each must have the right to judge spirits and prophets; but no one has the right to take the sword for himself. Otherwise what need would there be of the public government?

There is a difference whether this concerns the past of the future, but also whether it contradicts God´s Word as written – You shall have no other Gods! – or whether it concerns a new word from God, which is still to be tested. The first is not permissible, whilst the other is out for testing according and in the framework of God´s Word already given:

Here one asks how Moses can forbid to believe a prophet who performs and foretells signs that will come to pass, when nevertheless in chapter eighteen (v. 22) he says that if what the prophet said comes to pass, it is recognized that this is the Word of God. I answer: This chapter thirteen speaks of a past Word of God that has already been received and confirmed by its signs, just as he says: “You shall not add to it or take from it” (12:32), and again: “Keep the Commandments of God, and hear His voice” (28:1). In the face of such a Word no prophets are to be received, even if it were to rain signs and wonders—not even an angel from heaven, as Paul says to the Galatians (1:8). Here, however, a prophet is written about who will give signs in order to introduce other gods. This is already contrary to the Word which has been received concerning the only God who is to be worshiped, and therefore he should not be heard. In chapter eighteen He speaks of a new Word which has not yet been received and is not contrary to the one that has been received; therefore He says there (18:20): “If a prophet shall speak in My name what I have not commanded, etc.” Such a prophet is not to be received unless he does signs, just as Christ confirmed His Gospel with signs when it had to be preached in a way that went beyond Moses. For God does not reveal any new Word unless He confirms it with signs.

God tests his people and therefore, we should be watchful and pray to not be misled by false prophets, erroneous teachings, heresies, blasphemy, enthusiastic sects etc. because that sad lot has even befallen saints of the church, who by God´s grace came back to their senses:

God does indeed allow a new word to be taught in order to test us, but He is faithfully at our side, so that no signs are done or that what they have predicted does not come to pass, as He shows in the case of Elijah with the Baalites (1 Kings 18:24). Just so Paul also says (1 Cor. 11:19): “It is necessary that there be heresies, that those who are genuine may become manifest.” So He also permits signs to be done contrary to the received Word, again in order to test us (just as Moses says here), whether we love Him with our whole heart. So far Satan has misled us with signs and lying wonders into the working of error, as Paul predicted (2 Thess. 2:11), when we admired pilgrimages, appearances of spirits, or certain healings near some graves, all of which was contrary to the received Gospel. Saints, too, have slipped here, such as Augustine, Bernard, Jerome, and many others, who set up orders and rules of works contrary to the purity of faith, and who would certainly have had to be condemned (as Wycliffe says) if they had not come to their senses and been saved by the richness of their faith in the midst of unrecognized error.

God wants to be worshipped in faith and truth – not with sacrifices, works and other man-made rules and customs without the Word of God:

Strange gods, we have often said and say again, are not only an external idol but much rather an erring notion or conscience devised about the true God. For as the conscience is, so is God. If you believe that God is worshiped by sacrifices of this or that kind, in this or that place, and that without a Word of God, then you have already lost the true God; and that notion concerning sacrifice to which you cling under the name of the true God is your god. If you believe that God is worshiped through cap and tonsure, poverty, obedience, fasting, food, or drink (since here you do not have a Word of God), then cap and tonsure, or that notion about cap and tonsure, is your god. Therefore just as you have an inner assumption about the cap in place of God, so you extend this outwardly and set up,wear, honor, worship, and value the cap as an external idol according to the likeness of the inner notion.

The true triune God is only known and worshipped rightly through His Word.

See, this is what it means to make and follow other gods; it means to worship gods whom you do not know, because you do not feel or understand that in the place of the true God you worship a notion and an idol. Nor do you notice how uncertain you are in that worship, and how you think or know nothing concerning the true God, since you think about Him without His Word. But He cannot be known or thought of except through His Word. So you see that every way of inventing and worshiping strange gods is nothing else than that godless notion by which we choose and believe that we can please God without the Word of God, by this or that work, at this or that place, by this or that rite, when He is not of that sort and yet under His name another is falsely concocted in the heart. From this follow various names just like those of the idols. Thus one is called Baal, another Ashtaroth, another Dagon, another Moloch, Peor, Camos; and there are other names. Just so our monks are named, one from white clothing, another from black; and by his name and work each is outwardly different from the others. These all are prophets whom their dreams deceive. They say: “Let us go and worship strange gods.” That is, “Let us choose new rites without the Word, under the name of the true God.”