“To paint the things of Christ you must live with Christ,” said the 15th-century artist Fra Angelico. He knew what he was talking about – he was a Dominican monk of such exemplary virtue that in 1982 he was officially beatified by Pope John Paul II. He was also a truly great religious artist whose frescoes at San Marco in Florence have influenced modern artists such as Mark Rothko. But is all holy art that holy?

From the dark ages to the end of the 17th century, the vast majority of artistic commissions in Europe were religious. Around 1700 this somehow stopped, at least when it came to art anyone cares to look at now. The great artists of the 18th century, and since, worked for secular patrons and markets. But in all those centuries when Christianity defined art, its genres, its settings, its content, was every painter and sculptor totally sincerely faithful in every work of art? Or were some of them just doing what they had to do and finding pleasure in the craft?

This question relates to another. What is it like to live in a world where everyone is religious? It is often said it was impossible to even imagine atheism in the middle ages and the Renaissance. This is so different from modern times that people do not even try to imagine it. Modern Christians blithely imagine a connection when actually a universal church meant a mentality so different from modern “faith” that today’s believers are as remote from it as today’s non-believers. Among other things it meant that while some artists “lived with Christ” and made art that searched their souls, others enjoyed the colours, the drama, the rich effects of religious paintings without thinking too deeply about the meaning.

Here are two contrasting examples from the National Gallery. Zurbarán’s painting of St Francis in Meditation (1635-9) is a harrowing and profoundly spiritual work. The face of a kneeling friar is barely glimpsed in a darkness that speaks of inner searching, of the long night of the soul. This is a true Christian masterpiece. But compare it to Carlo Crivelli’s painting The Annunciation (1486) in the same museum. Crivelli’s picture is a feast for the eye. Potted plants, a peacock, elaborately decorated classical buildings – and is that a gherkin just added in at the front of the scene? – add up to a materialistic cornucopia of visual interest. What is the religious function of such detail? Art historians, who sometimes seem to be high on piety, will point to the allegorical meaning of everyday objects in Renaissance art. But that’s all nonsense. I am not saying the allegories do not exist – I am saying they do not matter much to the artist, his original audience or us. In reality, Crivelli is enjoying himself, enjoying the world, and he paints religious scenes because that’s what he got paid to paint.

By smothering the art of the past in a piety that in some cases may be woefully misplaced, its guardians do it a disservice. Is Crivelli a Christian artist? Not in any sense that is meaningful today. He loves the things of this life, not the next.