The question is a bit perplexing, as the Mannerist period of art and architecture (1520-1580) did not emerge from any fear or anxiety about the future of Europe or of man; it grew out of concern that the earlier Renaissance artists, mainly da Vinci, Michelangelo, Titian and Raphael, had taken art as far as it could go. The brilliance of those men and their contributions to the arts and to the sciences (particularly in the case of da Vinci), left many aspiring artists depressed about what, if any, contributions they could make in the wake of their predecessors. As the late art historian Ernst Gombrich has written, however, there were some who saw this as a challenge:
"Many, indeed, doubted that art could ever come to a standstill, whether it was not possible, after all, to surpass the famous masters of the former generation, if not in their handling of human forms, the, perhaps, in some other respect. Some wanted to outdo them in the matter of invention. They wanted to paint pictures full of significance and wisdom..." [The Story of Art, 16th Edition]
As a result of this development, the so-called Mannerists experimented with shapes, settings, perspectives, light, and every other aspect of a painting. Mannerism spread across much of Europe and influenced a great many artists, including Bronzino, Guiseppe Cesari, Correggio, and many others, few of whom would become household names like those whose styles they sought to surpass.
To the extent the question is directed more towards political developments occuring during this period, the sacking of Rome in 1527 by Charles V, who designated himself Holy Roman Emperor, and the first sparks of the Reformation were certainly notable events. The Catholic Church's response to the Reformation was the Counter-Reformation, which manifested itself partly in attacks on Renaissance art. Mannerism did proceed, however, so whether these are the causes of "nervousness" to which the question refers, this educator cannot say.