The burden of proof rests with those who claim that such things actually exist. Now this is the problem indeed, for the world of science seems to believe that everything can fit into its affairs because one day everything will be explainable by science. But when religion adopts a similar view for itself, well then we have an uproar that religion is wandering outside its boundaries. You draw the line between what the evidence can support and what it cannot support. The scientific method is used to define the exact location of such a line.
Religion attempts either to claim that no line exists or it disputes what belongs on which side.
I believe we can't segregate such important views at life. And while there are many who can only see far enough to take one view are the other, I believe there are many more who are willing to try to see with both sets of eyes and hopefully to get the picture. The problems are exacerbated when that same person decides to posit his view as either equal or superior to any or all others. I have no problems with what any person decides to believe for himself. But, when he attempts to challenge the views of others or to force his views upon them, then they must accept the responsibility to subject those views to the same standards of evidence that apply to all others.