What I find even more disturbing is that there is not a level playing field when it comes to solid, mainstream (in a good sense), scientific thought, and "anything goes", incoherent, sloppy or fake scientific thought. This is independent of naturalistic or supernatural worldview. For example, hypotheses about continents that sank in to the ocean in a single day millenia ago, are completely compatible with a naturalistic worldview, although one would really have to stink at geology to believe them.
Let's hold a thought experiment. Present to a friend a really blurry photograph, and claim it is you with Miss Universe (or a male equivalent) in a romantic date. The response you are probably going to get is that even if they were very willing to believe you (they're almost certainly not), the evidence is of very low quality. Now present to a friend a really blurry photograph, and claim it is a 7 meter monster which lives in the bottom of a medium-sized lake on an big island. In this case there is actually some hope that the response will be: "It could be. After all, there are so many things out there we don't know about...".
What's wrong? Same evidence, different responses. Is it that the existence of the monster is more probable than the existence of Miss Universe? It should be the other way (again, if you're not really bad in Biology and Ecology). I'm not sure what's wrong. What I know is that I have a hard time when I have to explain simple scientific facts like this one to friends or students (and this is exactly what is supposed to happen. They shouldn't buy anything I say) but the same people seem to be very easily convinced by the TV-show kind of "science", which claims it rewrites science textbooks every week.
So, if there is such a thing as "mainstream" or "established" science (I think it's nothing more than hypotheses with evidence supporting them), it should not seek priority, or precedence over "alternative" science (another name for hypotheses without evidence supporting them), but a level playing field. Same quantity and quality of evidence scores the same number of points.