Final answer:
The German princes adopted Lutheranism despite the Emperor's prohibition due to the Peace of Augsburg, the need to legitimize their rule, and the spread of Luther's ideas through the printing press and literacy.
Step-by-step explanation:
The German princes chose to adopt Lutheranism despite the Holy Roman Emperor's prohibition due to several factors. Firstly, the 1555 Peace of Augsburg granted rulers in the empire the right to establish their chosen religion within their lands. This meant that Lutheran rulers could make Lutheranism the official religion and their subjects were obligated to support it.
Additionally, Luther's ideas resonated with the German princes as they sought to legitimize their rule and integrate themselves with their population. Lastly, the printing press and increasing literacy in Europe helped spread Luther's teachings and accelerated the spread of Protestantism.