For a few years there, the indie rock world couldn't get enough of Cold War Kids.

The Los Angeles quartet's best-loved songs, Hang Me Out To Dry and Hospital Beds - performed on dark, loosely tuned piano and sung with Jeff Buckley-esque desperation by frontman Nathan Willett - became radio staples and created international demand for the band's live shows.

While touring between 2006 and this year, they crossed the US five times, Europe four times and had one "incredible" trip to Australia, all to promote a single album, Robbers & Cowards.

"We just kept on touring and it got to a point where we were asking each other: 'How long are we gonna keep this up?' " Willett says on the phone from his home in Long Beach, California.

The band has finally returned home, Willett says, to record a follow-up LP. He is enthusiastically trying to steer our conversation to details about their new album.

With a mix of nerves and cunning, I'm trying to manoeuvre our conversation to more controversial territory: God.

During those two years of touring Robbers & Cowards, the murmuring in the indie rock press about Cold War Kids' religious views grew to become the main talking point. The revelation? That three of the four bandmates met while studying at the Bible Institute of Los Angeles.

Marc Hogan of indie music blog Pitchfork Media first "outed" the band as Christian rockers in disguise. In his review of their LP, Hogan asserted the band's songs were sermons. Lyrics such as "put out the fire on us" from Hospital Beds, he wrote, "signify a call for baptism". Passages such as "all us boys on death row, we're all waiting for a pardon" from Saint John "is a reminder that we're each of us sentenced to die unless we accept God's redeeming grace".

As Hogan's accusations spread, the Cold War Kids' fanbase splintered. Could indie rock - a genre with an unspoken code of defiance and godlessness - accommodate students of institutionalised religion?

A few commentators came to the band's defence. Britain's NME said the album was only proof "Christians make great storytellers", rejecting suggestions the album contained any "holy Joe preaching".

There were plenty of haters, too. Evangelical commentators such as Seattle pastor Matt Johnston accused the band of "being dodgy about faith", which in his view "smacks of a cultural inferiority complex". Other Christian acts traversing the indie world (such as Sufjan Stevens), Johnston suggested, suffered less by acknowledging their faith from the outset.

Here is Willett's chance to set the record straight.

No, Willett says, Cold War Kids are not trying to preach to anybody. "You have to maintain this constant balance as a songwriter," he says. "Our songs are all written from the perspective of characters - and while those characters are born of my mind, they are not songs about me. Our own views on religion are not things we write songs about."

Rather than let it upset him, Willett sees the Pitchfork review and reactions to it as "a very interesting sociological phenomena" to study.

"Even if we put it outside of ourselves and just observe it for what it is, this is so interesting," he says. "As you say, the indie rock world has a problem with Christianity. It was so interesting to see how seemingly tolerant that world is on the surface but how intolerant and inconsistent it really is underneath.

"And the whole time," Willett adds, "it's been incredible how little anybody has ever asked us about our views."