Luther was different from many of the other radical populist movements like the Lollards in that he was generally supportive of the secular powers of the time and supportive of commercial enterprize and private wealth. His moral teachings are very 'common sense' and supportive of traditional structures like marriage and family, nothing radical. As such he developed a following among the burgers, a growing and increasingly wealthy class of traders and artisans not included in the Catholic aristocracy power structure.

This was greatly appealing to many of the minor nobles in the Holy Roman Empire, where large wealthy states maintained regional hegemony often with the explicit help of the Catholic Church, resulting in widespread discontent with corruption and exploitation. Protestantism was the wedge many minor nobles needed to free themselves from political intrigues of the bishops and creating their own power base.

The best example perhaps is the first. Frederick III, Elector of Saxony became one of the most important early supporters of Luther, allowing him a safe base to attract followers, preach, and disseminate his writings. While Frederick gained potentially as a leader of the new Protestant faction, much of the power behind the throne came from the wealthy Pfaffinger family (look up their descendants!). Once he was in their service he was able to devote most of his time to writing and developing his worldview, as he was pretty much prevented from traveling anywhere once the reformation was in full swing after the Diet of Worms.

But what really helped him was his ideological service to his new benefactors. When radical revolts broke out in the south during the Peasant's War he decried the worldly political aims in "A Sincere Admonition" and the "Invocavit Sermons" where he basically said violence and force were unchristian (but that obeying laws of worldly rulers was an obligation).

This same pattern repeated all over the HRE: where local guilds, merchants, or cities had wealth and power to overthrow a weak aristocracy, they often would adopt Lutheranism - often the case in the north and Hanseatic cities. Where the Catholic aristocracy or church itself had more power often these movements were suppressed or expelled. Because this is the HRE, though, obviously there is a lot of heterogeneity, on all sides.

The key to most of these movements at the heart of your question is that in order to have a lasting religious movement in old Europe it was key to secure the support of local political powers. At the time of Martin Luther there was a wealthy class with political powers, and political powers maintained with religious traditionalism. He was just religiously radical enough to invert this political power situation, but still conservative enough to prevent complete change in the underlying structure of power.