IThere is no doubt that Bruce Bannar is religious. As one of the main members of The Avengers, Bruce is one of the known religious few.

 

What comes to question is his alter ego. Bruce rarely has control over The Hulk, and in the brief moments when Bruce's mentality and personality come through to The Hulk, he acts like a normal superhero, but most of the time Hulk is destructive and uncontrollable. 

 

Through the comics and films you can see Bruce being a religious man, he marries an (almost) nun, in a Catholic church (which is only allowed if both parties are Catholic) - this doesn't prove he practices regularly, but it does prove that he was raised as a catholic. 

 

What mainly shows his beliefs and faith is his "death." 

 

In the comics, Iron man places Bruce's rosary beeds in his unconscious body (appearing dead).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Bruce doesn't ever speak of what his true beliefs are, however he once stated to be a lapsed Catholic, he is mostly portrayed as a non-religious scientist. in the live-action movies Bruce is seen practicing meditation to try and control his alter-ego, but meditation isn't always associated with religious practices, it's sometimes just used as a relaxation tool which I believe was Bruce's intention.

 

It's hard to say what Bruce's beliefs are, but when he faked his death in the comics, there was a good indication of his true beliefs. 

 

In Bruce's self written ulogy he expresses that his religious beliefs are "private" but he does believe strongly in an afterlife for the human soul.