William Shakespeare probably knew the ancient Roman world better than most of us. For this reason, he knew how important religion was for the Romans. The Romans above all else wanted to keep the pax deorum, the peace of the gods. Hence, they would have elaborate rituals when they thought something went awry. Julius Caesar would have known all of these things very well. After all, he was the chief priest in Rome - Pontifex Maximus.
In light of all these point, one of the ways Shakespeare shows the foolishness and "evil" of Julius Caesar is that he completely neglects the gods.
Let me give you several examples. When the soothsayer says to Caesar, "remember the ides of March," Caesar simply ignores him. The soothsayer constantly says this, but it is to no avail. Everything falls on deaf ears. In addition, before the assassination, there are prodigies and omens. Caesar again ignores them. A good Roman would have reported these to the senate and ascertained why the gods were angry. After this action certain expiations would be performed. Finally, Calpurnia even has a nightmare and warns Caesar, but once again Caesar ignores this sign.
In the end, Caesar neglects the gods, one of the most impious things a Roman can do.