To begin with, this is a challenging and nuanced question, asked by a Christian student of philosophy, history, and religious studies. I'll try to be a little nuanced but not overly challenging in my answer.
The Lutheran Reformation arose during a time when Chrsitian mysticism was common. To assist in our analysis, we should point out that mysticism regularly involves an interest in intangible ideas, regularly interpreted by considering our inner life of thoughts and emotions. The mysticism of the later Middle Ages typically evaluated reality based on dreams, visions seen in times of prayer, and sometimes recognizable supernatural gifts. The writings of the mystics were often held up as examples of deep spirituality, though they were condemned by some. As Chrsitian mysticism, the philosophy is tied in some way to Chrsit's atonement or some other work of God.
Because mysticism is almost uniformly self-mediated, it comes into conflict with two major tenets of Reformational thought. First, it brings human intuition into the mix we normally recognize as Sola Scriptura - Scripture alone as our definitive revelation. This is a substantial problem. In Lutheran thought, Scripture is recognized as a gift of the authoritative Word ofGod (John 1:1-5) which is necessary for the very existence of the world. It is useful in this life (2 Timothy 3:16-17). It is to be valued above all else. Mysticism elevates human reason and intuition to a level equal or superior to Scripture.
A second way mysticism conflicts with Lutheran thought is that, rather than finding God's provision in something "outside ourselves" (extra nos), we are urged to look within. Because of our fallen nature and the strong inclination of our nature to flee from God's will, mysticism is more likely to lead us astray than to confirm us in Christ.
Martin Luther, in the first of his 95 Theses, said, "When our Lord and Master Jesus Christ said, 'Repent' [Matt. 4:17], he willed the entire life of believers to be one of repentance" (Luther's Works, American Edition vol. 31, p. 25). This requires that we look for a source of authority outside ourselves. It means we accept the Word of God as our guide, rather than our own human wisdom.
So Lutheran thought is normally very suspicious of mysticism. The mystic looks to his inside, while the Lutheran theologian of the cross looks outward.