One of the first instances I can think of is the Carmina Burana - no, not Carl Orff's 1936 work, but rather the 11th and 12th century text that he drew his lyrics from. The Carmina Burana contains songs by the Goliards, a sect of the clergy who we see were very critical of the Catholic Church, particularly in their abuse of simony and penchant for greed.

A more mainstream example that comes to mind is probably the emergence of opera buffa (comic opera) in the early 18th century. Because the intended audience of opera buffa was the middle classes (as opposed to opera seria, which was created largely for the aristocracy and royalty), librettists (story writers) often strongly satirized political conditions of the day. Since the scathing, lightly veiled commentary was couched in music, humor, and costumes, the underlying message was able to slip past typical censorship and into the mainstream.