Unshakable Beliefs

I've heard people talk before about being pyschologically incapable of not believing in God. I've heard the same from an atheist or two. Or the case of parents refusing to believe their child has done something evil (murder, rape, etc.), in the face of overwhelming evidence.
It truly is a bizarre phenomenon, is it not? A belief which we cannot rationally reject. I've never really completely understood it, as I couldn't analyze a situation in which it had happened to me. But now, I have realized a belief I do have which is unshakable. My belief in karma.
Now its strange--I was raised Catholic--why karma? I'm not sure, it probably has something to do with Catholic guilt. So I don't believe in karma. I don't think that people who commit bad acts necessarily 'get theirs'. Some people live terrible lives and have only luck. Some people live great lives and have only shit happen to them. And sure, in a lot of cases the opposite happens; sometimes evil people do get theirs, and sometimes good people do as well.
But karma just doesn't fit in with my worldview. I don't see it. It doesn't fit in with science, and I'm agnostic, so I can't appeal to some God guiding things along--not to mention karma isn't really consistent with the Christian doctrine (well, they believe in karma, but it comes after death, not before.)
Yet despite my complete acknowledgment and rejection of karma on a rational level, I find myself with unshakable beliefs. When I act in a way I perceive to be immoral, or hurt someone, I find myself having the unshakable feeling of impending doom. Something bad will happen to me. I will be punished. It can be terrible.
I guess this just illustrates the close link between emotions and beliefs. Most philosophers (myself included) are in a constant battle to separate emotions and beliefs--rightly so, as this provides an example of where emotions cause irrational beliefs. In lesser cases, it happens unconsciously. That is why all beliefs ought to be justified, all the way down to self-evident beliefs.

But my question is: What do we do about these unshakable beliefs? Do we fight them? Try our best to ignore them? Embrace them?
I really don't know. I think that all of these could be correct. I mean, take for example, a person who has an unshakable faith in God. Why not embrace it? It gives them piece of mind, hope, hopefully causes them to do good things for others, etc. But it can only truly be a positive thing if this embrace comes with a healthy realization that the belief's unshakability does not equal its truth--as I stated above, some people have the unshakable belief that there is no God. So clearly unshakable beliefs are fallible.
Now as for fighting them, Yes, we should always fight beliefs we believe to be irrational. An irrational belief is one that is unlikely to be true, and a false belief will very rarely help us with anything. (That God example is pretty much the only one I can think of.) But, clearly, if the belief is truly 'unshakable', as we've defined it, fighting it will not be of any use.
So in certain cases it seems that we should try our best to ignore them. Take the person who has the unshakable belief that Their life is meaningless. They probably should ignore that rather than embrace it--otherwise they will probably kill themselves.

But I guess the main thing is that if you truly have an unshakable belief, you ought to use it to your advantage, as in the God example. The problem is that people become dogmatic--they think unshakability equals truth. And this is where fundamentalists come in, from homophobic funeral protesters to Muslim terrorists.

I believe we have an epistemic duty to constantly look for evidence that may challenge or reshape our beliefs, especially the ones that, if false, could do a lot of damage; for example, ethical or political beliefs. This is what motivates me, when I'm having my week long bouts of moral antirealism, to continue researching, to continue asking myself "Well, what if I'm wrong?"
Hopefully this will do me more help than harm.

And, as for my unshakable belief in karma, I despise it, but I try best to use it to my advantage: as a deterrent for acting unethically. All the while, continuing to try and shake it off as irrational.