Another Republican heavyweight has fingered religious conservatives (or the oogedy-boogedies, as one conservative called them) as the culprits in the GOP loss. Jeffrey Hart (former aide to Nixon and Reagan and longtime contributor to National Review) writes:

George W. Bush transformed the center-right party of Richard Nixon, Ronald Reagan, and his father, George H.W. Bush, into the political instrument of the religious right… In 2000 Bush-Cheney got 75 percent of the white evangelical vote.

This has had significant political consequences: federal funding for all embryonic stem cell work was blocked; federally funded faith-based initiatives (abstinence only) were begun; and the theory of evolution became politically controversial for the first time since the 1920s.
In a speech in Irvine, California on April 24, 2006, Bush even gave a religious reason for the Iraq war.
‘I based a lot of my foreign policy on some things I think are true. One, I believe there is an Almighty, and secondly, I believe one of the great gifts of the Almighty is the desire in everybody’s soul, regardless what you look like or where you live, to be free. And I believe liberty is universal. I believe people want to be free. And I know that the best to defeat the enemy, the best way to defeat their hopelessness and despair, is the ability to give people the chance to love their life in a free society.”
In that glimpse into his muddled thinking, almost everything Bush said was shown to be false.

Crunchy Con rebuts:

McCain lost because the economy is collapsing on the watch of an unpopular Republican president, and he had no idea what to say about it. McCain lost because his party is incompetent. McCain lost because his choice of Sarah the Unready cast doubt about his judgment. And McCain lost because Barack Obama ran a great campaign.
Where is Jesus in any of that?

I agree with Crunchy that. religious conservatives are being scapegoated.
However, I do believe that on balance religious conservatives hurt the ticket for three reasons:
1) Their influence led to the selection of Sarah Palin as VP. She cost them more than she gained them.
2) Religious conservatives (or fear of them by McCain aides) prompted McCain to avoid several candidates who might have helped with big states or with the economic message (Michael Bloomberg, Tom Ridge, Mitt Romney, Charlie Crist). Try to imagine how different the conversation about McCain and the economy would have been had Bloomberg been the VP candidate.
3) Immigration. My reasoning is a bit circuitous but the gist is: if McCain had kept to his original moderate view on immigration he could have won Latinos and proven his maverick bona fides. He didn’t, because he probably couldn’t have gotten the Republican nomination. One reason is that religious conservatives who dominate the primaries are particularly anti-immigration. (More details on religious conservatives and immigration here).
To win, Republicans can’t expel Religious conservatives — and religious conservatives should not trim their sails in what the push for — but Republicans need to know when to say no to them, like any other constituency.