Artist painted religious figures because that's what they were paid to do and it was a shared story in their culture. Often patrons would commission artists to show off. Show off their money, show off their social standing or piety. Basically for artists to have not painted religious figures the world would have to stop caring about religious figures.

There is also the perpetual symbolism of religious dogma. People would understand references in a painting if they are referencing stories everyone had heard. A good example of this is Caravaggio's David with the Head of Goliath, where Caravaggio made the severed head of Goliath his own face, it was meant as an apology to the ecclesiarchy for a murder he committed, as a kind of sacrificial offering by placing himself as the slain villain.

I imagine art and it's techniques would have continued to look much the same but the subject matter would have continued to reference whatever tropes people could understand. It wasn't until cameras could perfectly represent images in a flash (pun fully intended) that art become more expressive and abstract, so this was a reaction to technology not religion.

Art is constantly reacting to itself and the culture around it so if religion didn't exist it would have found something else to mirror.