What it took a long time to come to grips with is that the vast minority of people don't trend toward logical thinking and nuance, but trend towards emotional thinking and easy answers. Even when people supposedly are "logical" in one area (ie. evolution), you can often see them abandon that in other areas that they personally hold close (things like social issues or relationship issues).
The only thing you can do is avoid directly "attacking" their beliefs, because people like that view beliefs as an extension of themselves and feel like you are attacking them, personally, but, instead, ask brief questions that might hopefully start a crack and create a chink in their armor.
For one personal example, my dad was a "weak" JW and questioned everything for quite some time. Then his mother died, and he went on full board and became completely illogical about everything he questioned before. After the point of his mother dying, questioning his faith meant questioning him ever seeing his mother again, and so any logic, etc. was immediately shut down.