While I wouldn't say all art from that period was religious...as some of it depicted historical and quasi-historical events (the Bayeux Tapestry, images of Arthurian lore, etc)...you have to realize that there was a sharp division of labor in Feudal Europe: you had the Nobility, the Clergy, a tiny Merchant class and the Peasantry which made up the vast majority of the population.

There certainly wasn't any opportunity for people to make a "living" producing personal and independent art. You needed a patron i.e. someone to feed you and clothe you while you painted or sculpted. In the Middle Ages the most common patron of the arts was the Church who saw great political and cultural value in 1. Creating works of beauty to inspire awe in the faithful coming to their Churches and 2. Using visual images to teach a mostly illiterate peasantry about Christianity.

It wasn't until the explosive growth of a Merchant class in the 1400s that you had a class of people with enough money to patronize artists and no specific goal to further religious dogma. Hence the Renaissance.