I was surprised and pleased to discover that the rock band Switchfoot have a song about the terrible cost to oneself of treating one's arguments as soldiers. It's called "The Sound in My Mouth". (Youtube link, with incorrect lyrics below it; better ones can be found at the bottom of this fansite page)

It focuses on the social costs rather than the truth-finding costs, but it's still well ahead of where I usually expect to find music.

If they believed(1), they would spend every waking moment exactly as their religion instructs.

That's too strong a claim and doesn't factor akrasia in; you might as well say that you don't really believe in the seriousness of existential risks if you don't spend every waking moment working against them.

You can, however, make distinctions between people who will make decisions that they know would be extremely suboptimal if their professed belief was false, and people who only do just enough to signal their belief.

It's going to be a continuum from belief(1) to belief(2), not a binary attribute; but it's still a very important concept and not yet one that the English language groks.