If the spiritual interacts with the earthly in any way, it should leave traces of it's activity. For instance, if Jesus himself were to show up in Tokyo, where there would be plenty of eyewitnesses to see it, that would leave proof. If God gives someone information, and that person had no possible way to access that information on their own, then thats proof as well (I.E. the location of buried treasure).
And since in religion God seems to show lots of activity in our world, where is the proof?