It is a devastating thing when you can't help someone you love. You inevitable end up hating whatever it was that prevented you helping. I can understand your hatred of superstitious hope, or skepticism/fear of medicine.
I know someone like your grandmother (at least, the particular details/traits you describe) - she would rather die, literally, than allow herself to be probed, or have her body invaded/cut-up/violated by scalpels. Fortunately, she doesn't seem to be suffering from any disease. However, as much as her stance is ridiculous to me, it is based on something I know all too well: personal boundaries/limits which act as a defense. What are they protecting? A sense of personal dignity.
Some people don't have a very secure sense of dignity - perhaps because they are physically diminutive, or something of an odd-bod; perhaps because they don't have the intellectual wherewithal to hold their own, or even to comprehend what others are discussing; perhaps because they are naturally timid, or have few family/friends they can count on. For many people, if not most people, their greatest source of strength is in their own unbreakable will.
People who feel vulnerable, or powerless - and that would be most of us at one time, or another - attach their wills to anything that in any way could seem a safe bet. For those who cannot understand, it is blind ideologies; for those who are physically vulnerable, it can be in obsessive preoccupation with defense (as martial arts, or technological defenses, etc.); etc. Attacking this 'anchor' they attach their will to, only reinforces it - in martyr complexes, or confirmation of threat assessments, etc. The worst tragedy is that the best defense is usually offense: those who are insecure often end up being aggressors... the whole victim, turned abuser phenomenon.
The only thing to help people who have become stubbourn as a defense is to help them gain a sense of their own security, safety, value, creative ability, beauty - a sense that they are loved, secure, and have a dignity that is intrinsic and cannot be taken away, and needs no defending.
The religion thing. I know that most people experience religion either as a blind ideology, or as a superstitious system, or as a means of evading hell - all of these things do provide people with a certain means of defending some sense of their own dignity (self-righteousness?). However, some religion is experienced as a friendship - a loving friendship with God, that dissolves fear and replaces it with the security of being loved - not the security of being stubborn. Love is never a closed off, close-minded thing.
I don't think critical thinking is anything but a good thing; however, defensive critical thinking - or worse, offensive critical thinking does nothing to open people to knowledge, possibilities, etc. Rather, it just contributes to a deep mistrust of everything/everyone.
