I don't necessarily think that "an identity of critical thinking" is the answer.

I've renounced beliefs, several times, that I thought were central to my identity, but weren't backed up very well by the evidence. The pattern was that I would think about what I actually wanted to protect -- what really mattered to me -- and found that it wasn't quite the same as the (false) belief in question, and that I could be truer to myself without illusions.

For example, someone who thinks capitalism is evil may, at root, be someone who really cares about preventing human suffering. You can still do that -- you can do it even better -- if you don't subscribe to inaccurate information. Same thing for someone who believes that socialism is evil -- it might be a person who really values autonomy. You can still do that without swallowing malarkey.