I still think that critical thinking has an important role here. You say "they didn't reason themselves into the position and you cannot reason them out of it".

I still think that critical thinking has an important role here. You say "they didn't reason themselves into the position and you cannot reason them out of it". This is correct and is actually what critical thinking is about: reason about something instead of blindly believe in something. If they were capable of critical thinking, they would have reasoned about it instead of blindingly believe in it. And while they could still reach the wrong conclusion, you could still try and reason them out of it.