Although isn't it much of it demonstrable only to the experimenter? I'll never see or fully understand the LHC for instance, so I take it on faith that those experiments are valid and repeatable (or that they even happened) because I trust the source who tells me that. When I talk to some of the more religious people I know, it's interesting to listen to their terminology: they say they "know" there's a God, not simply that they believe or hope, precisely because they've experienced a change within themselves and claim that that experience is as real to them as any physical experience. I can't say that I deeply, fully understand either science or religion, so looking at each from the outside it's difficult to explain why I innately trust science more (which I do). I could argue that it's because science at least offers the promise of testibility: if I were to devote myself to it I would see that this method works in a repeatable way. But really, the religious folks often say the same, that if you accept it you will experience something undeniable and on the other end you'll know that God exists.
More than anything, I think this all just highlights the importance of critical thinking. Continually question and test the whole chain that leads from a system of belief to you. Because it's not just science that we sometimes have to take on faith, it's everything around us, from news and politics to the idea that what I can't see continues to exist when I'm not here, or that I'm not just a brain floating in a vat somewhere.