Yes, I know it's a comic... but these heroes are today's modern mythology. I'm not sure if anyone cares what Bruce Banner or Bruce Wayne believe theologically, but I like to explore the 'what ifs'. They're bound by their mediums at times and therefore can't change their ethics much, eg. Batman can't 'kill' the Joker, (even though he should) because we'd run out of decent bad guys. I think this is ummm.. bemusing? Plus I like to get 'green' pictures on my blog for aesthetic reasons...
Bruce Banner's overriding passion at times appears to be science. But even Banner's love for science is often subsumed by his complex anger and peculiar psyche that gives rise to his monstrous alter ego. Banner also appears to be a classic narcissist, as he usually appears to be more concerned with his own problems and his "cursed" life, often with seeming disregard for the lives he has destroyed (including the people closest to him) and the many people, including soldiers and innocent bystanders, he has doubtless killed while transformed into the Hulk.
So, it is possible that Banner's failure to kill himself might be a result of a narcissism and pure secular materialism. Or his choice might stem from deeply held Catholic beliefs and fears regarding suicide. Thus, this aspect of the character can not really be used to identify his religious affiliation or beliefs. A truly utilitarian secular humanist, for example, would almost certainly feel compelled to commit suicide if he posed such a danger to society, and many religions and denominations do not have the strict teachings against suicide found in Catholicism.
One explanation for why Banner does not destroy himself looks to all the positive things the Hulk has accomplished. As John McDonagh observed: "While the Hulk does cause damage, he for the most part does not rampage across planets or dimensions. However, he has opposed creatures who are much larger threats than he himself is, threats to solar systems and so forth. Therefore, he must continue to exist to stop Thanos, the Galaxy Master, etc."