It sounds nice in theory. But "teaching facts and facts and beliefs as beliefs" makes about as much sense as deliberately wanting to undermine everything you actually believe in.1) That's why I said we should teach each one according to what it is. Teach facts as facts; teach beliefs as beliefs. Although I think you're underestimating how many facts there are.
2) Yes, a lot of people do believe their beliefs are facts, and that's something that would be nice to do away with.