This is not wise. If we offer the religions in chronological order, and pay close attention to the world situation, especially the situation in Europe, we'll see something that most people miss. Lutheranism owes a heavy theological debt to Mohammed.
Now, to be fair to Luther, he recognized Mohammed as an Arian heretic who denied the divinity of Christ and called the Koran a book of Satan.
So it's not like he LOVED Mohammed.
He didn't like him at all.
But, that having been said, there are several points of contact between Islam and Luther's teachings.
1) War Against the Turk is War Against God
Both Islam and Luther agreed the fighting the Muslim army was fighting God, although they thought this for different reasons. For Muslims, they really WERE on a mission from God because they were the true faith. After all, they started a rampage against Christians in 632, crossed into Spain in 711, conquered Constantinople in 1453, and headed up to Buda and Pest about the time Luther was hammering theses on a church door.
However, from Luther's point of view, as represented in his defense of the 95 Theses, while Muslims were an heretical faith based in Arianism, they were also sent by God to scourge Catholic Europe, so no opposition should be brought against them. This was especially true given that Luther held that the Pope was more evil than Islam. So, while the Pope was trying to gather Christian armies to fight crusades against Muslim rapacity Luther was actively trying to keep any Christian from fighting. Luther only began to modify his stance when the Muslims finally captured Buda and Pest, and began to advance on Vienna.
2) Iconoclasm (the destruction of images)
Both Islam and Lutheran Protestantism destroyed images because they argued that God commanded it. For both, the use of images was idolatry.
But again, to be fair, Luther and his compatriots were not the first to be taken in by the aspect of Muslim theology. The Eastern Christian Church in Constantinople underwent at least two different bouts of iconoclasm between 700 and 1000 AD, both a result of the fact that Muslim armies were constantly attacking the city.
Within 100 years of the first assault, the Christian emperor of Constantinople decided to join his Muslim opponents in destroying images, the beginning of the great Iconoclasm heresies. In both outbreaks of iconoclasm, it took decades to put down the heresy.
So, we should not be surprised to see Protestants changing the teaching on Decalogues' teaching on images as Muslim armies attacked Budapest, in much the same way the Eastern emperor had when Muslim armies attacked Constantinople.
3) The Irrationality of God
In both his sermons and in the collection of sayings called Table Talk, Luther stated:
"But since the devil's bride, Reason, that pretty whore, comes in and thinks she's wise, and what she says, what she thinks, is from the Holy Spirit, who can help us, then? Not judges, not doctors, no king or emperor, because [reason] is the Devil's greatest whore." The original German is "Vernunft ... ist die höchste Hur, die der Teufel hat" Martin Luther's Last Sermon in Wittenberg ... Second Sunday in Epiphany, 17 January 1546. Dr. Martin Luthers Werke: Kritische Gesamtausgabe. (Weimar: Herman Boehlaus Nachfolger, 1914), Band 51:126, Line 7ff
Islam, of course, has always taught that Allah is not bound by rationality. He is more powerful than anything, even the force of reason.
Now, Islam teaches that God can change, while Protestantism has never taught this, but that's only because Islam is more theologically consistent than Protestantism in this regard. After all, if reason really is the "whore of the devil," then God cannot be rational as His very rationality would make Him the devil's whore. Lutheran theology in reference to the role of reason and faith is essentially just a restatement of Muslim theology.
4) Divorce is Legitimate
Muslims always permitted divorce - the man simply says "divorce" three times and that accomplishes the deed.
Once Luther became convinced that marriage was not a sacrament (which was the Muslim position as well, of course), Bucer became the first Christian to draw the logical conclusion. He argued as the Jews and Muslims did, that marriage was simply a civil contract, and divorce was a reasonable solution. Protestants in general and Lutherans in particular quickly followed suit.
5) Polygamy is Acceptable
But even divorce was sometimes troublesome. Luther asserted that nothing in Scripture forbad polygamy. Bucer, Melanchthon and Luther would all advise Henry VIII to simply commit bigamy instead of going through the trouble of annulment when Henry tired of his wife. Henry had not the stomach for the Protestant solution, but that didn't stop the idea.
When Philip of Hesse faced the same problem, Luther famously advised him in the same way - simply take a second wife secretly when he tired of the first. Philip acted on the advice and did so with Bucer and Melancthon, Luther's main theological advisor, serving as witnesses to the "lawful" bigamy. John of Leiden had reached the same conclusion in Munster just five years earlier, and the whole city had become bigamous for a time, so Luther wasn't even original in this advice. http://en.wikipedia.org/wiki/Philip_I,_Landgrave_of_Hesse#Bigamous_Marriage
6) Lying is a Virtue in Times of Necessity
A standard of Shi'a Muslim theology is the practice of taqiyya, or lying in order to protect the faith. Luther gave similar advice on the virtues of lying to Philip of Hesse when Philip's bigamy was found out. Unfortunately, the lie was found out as well, and Luther's reputation suffered somewhat from the resulting scandal.
7) Proclaim With Your Mouth
This last is not really Luther's fault - to the end of his life, he insisted on the necessity and efficacy of baptism. However, his rejection of the other sacraments and his sole fide theology led naturally to a very Muslim conclusion: the sinner's prayer is efficacious.
Everyone knows that in order to become a Jew, the man must be circumcised. What most people don't realize is that conversion to Judaism requires a ritual bath: the mikveh.
That's why John the Baptist baptized people - he was giving them the ritual bath that signified the conversion of hearts. While neither the mikveh nor John the Baptist's baptism did anything in terms of grace, that wasn't true of the baptism Christ instituted. For 1500 years, baptism was the sacrament which fulfilled the symbol the mikveh represented. It provides sanctifying grace.
But nearly a millennia of Muslim violence changed many people's idea of what was necessary to convert to a life of faith.
"Laa ilāha illa Allāh, wa Muḥammad(un) rasūl Allāh." Say that sentence aloud and, according to Muslim theology, you are thereby rendered a Muslim, subject to all shariah law, including the law which makes apostates eligible for the death penalty.
Similarly, 19th and 20th century Christianity adopted this Muslim concept and came up with the "sinner's pew" - the first pew in the church, a place reserved for those the preacher intended to focus his conversion sermons on. That, in turn, became the "sinner's prayer."
Proclaim with your mouth that Jesus Christ is Lord, believe in your hearts that He is risen from the dead, and you are saved. Not only is that sentence very close to a passage in Romans, it is virtually Muslim in its sentiments.
If you have ever wondered why secular humanism - the fruit of Protestantism - is so favorable towards the Muslims, this may give some of the necessary philosophical connections.