Michelangelo's sculpture teacher Bertoldo di Giovanni was a resident of Lorenzo de' Medici's household, which was an important center of Italian Renaissance art and culture. Lorenzo was the unofficial leader of the Florentine Republic, a man who wielded great influence due to his enormous wealth and his dedication to the city. Lorenzo de' Medici's patronage of many artists and thinkers made Florence the epicenter of Italian culture outside of Rome. Lorenzo de' Medici was himself a poet and an architect as well as a politician and businessman, and he represented to the Florentine people the balance of different interests and personalities that they so revered.
Therefore, it was a great honor for Michelangelo when Lorenzo the Magnificent, most likely acting on di Giovanni's advice, invited the fifteen-year old artist to stay in his palace in 1490, both to learn and to serve. Lorenzo de' Medici was always interested in young and talented artists, particularly since making their acquaintance often proved to be useful for Florence and for de' Medici's own image as a preeminent patron of the arts. Michelangelo accepted the offer, and de' Medici gave the boy a stipend and the father a clerk's position in his household. Michelangelo was always proud of the formative years he spent in the Medici household, since it removed him at an early age from the traditional apprenticeship in an artist's studio and put directly in the service of a famous patron.
Lorenzo de' Medici was impressed by Michelangelo, and raised him with his own family. Two Medicis later became Popes–Lorenzo's son Giovanni, who became Leo X; and Lorenzo's nephew Giulio, later Clement VII–and both would employ the artist they grew up with. The influence of the humanist and Neoplatonic thinkers in the Medici palace on Michelangelo was also profound. Among others, he met the painter Sandro Botticelli, the poet Angelo Poliziano, and the literary historian Cristoforo Landino, and these men provided Michelangelo with an informal continuation of his scant education informally.
Michelangelo also came in contact with the philosopher Marsilio Ficino, the foremost thinker of the Neoplatonist school of thought which would greatly influence the High Renaissance. Neoplatonism, an interpretation of the ideas of the Greek philosopher Plato, held that there was one universal Truth, which could be expressed on Earth through a number of different forms. This philosophy was used as the basis for symbolic synthesis, wherein artists mixed Classical and Christian forms and content in their works. Neoplatonism was later censured as heretical during the Counter-Reformation, which frowned on secular or Classical works. Michelangelo was also, however, exposed to the religious fervor of Girolamo Savonarola, a Dominican friar who was eventually burned for his militant opposition to the tenets of Neoplatonism. This may explain why Michelangelo's opinions on Neoplatonism were conflicted, and why he wavered on the issue for much of his life. Throughout his life, the devout Michelangelo felt very conflicted about religion.
Two very different relief carvings survive from this period of Michelangelo's life: the delicate Madonna of the Stairs and the dynamic Battle of Centaurs. Lorenzo de'Medici died in April 1492, at which point Michelangelo left the palace briefly to study anatomy at a nearby hospital, where he learned to dissect human corpses. Lorenzo's successor, Piero de'Medici, invited Michelangelo back to the palace and he returned, beginning work on larger marble pieces.
I think the time when the Council of Trent condemned naked pictures was in Session XXV on December 4,1563. The public domain translation of the Council of Trent by Tanner says, "Furthermore, in the invocation of the saints, the veneration of relics, and the sacred use of images .... all lasciviousness avoided, so that images shall not be painted and adorned with a seductive charm"