I was in Riverside earlier today listening to Richard Carrier speak, and one of the questions was concerning whether theists cared about the truth because some argued they did and others argued they don't really. And Dr. Carrier made the point that that is what makes it a fantastic wedge issue. It wasn't elaborated on, but certainly it's accurate, and has always been the rather core issue with religion.
If you care whether your beliefs are true, then there are a set set of things you should do. You should find a way to determine if something is true or false. You should find methods and a methodology by which you can determine what is true and what is false. And when you care about truth, your beliefs must always live and die by the evidence. Following closely from the desire to believe what is true is the requirement that we rely on evidence and reasonable argument. And that's a rather stunning trap. Because if one limits themselves to reasonable arguments and evidenced facts, you've cut off all paths that could get you to theism.
The want for truth isn't very hard to illicit from believers, so they really do care whether their beliefs are true or not. But, if you dig a bit with regard to their religious beliefs, this nice metric developed ad hoc suddenly becomes a heresy when you ask it to be applied to religion. On one hand theists want to accept what is true and not accept what is false, but on the other they don't care about the evidence at all or anything you say because they want to believe. And if they do that, they are accepting something less likely to be true over something more likely to be true, while they are allowed to do that, it's a rather serious problem. And if they are stuck there confronting their own cognitive dissonance it's not too much harder to ask them to admit that your position (not accepting any gods) is a perfectly valid one to hold because, after all it's more reasonable than theirs. They can try to weasel out at any point but they are damned if they do and damned if they don't. If they abandon the epistemological metric developed then they don't care whether what they beliefs are true or not. If they insist that there evidence matters, then the lack of evidence for theism in general or Christianity in particular is a serious problem, and the absence of evidence makes reasonable an absence of belief.
Treating "caring about truth" as a wedge issue forces theists to either abandon faith as an argument, or accepting that accepting faith as an argument means abandoning truth as a desire. They accept God as true on faith, and admit using faith as grounds means they don't care about believing true things. Or they can accept reasonable evidence alone which means they need should have a reason to believe resting on sound evidence and argument.
Finally, what does it say about the state of intellectual discourse in religion if "caring whether you believe true things" is a plausible wedge issue?