Naturalistic Paganism
Naturalistic Pagans seek to integrate ritual and meditative practices with a mythic worldview based on the most current and compelling scientific evidence. Most Naturalistic Pagans consider the scientific method to be the most reliable guide to reality, more reliable at least than faith in ancient religious texts or the spiritual visions of individuals. In general, “science” refers to the pursuits and findings of the mainstream scientific community, which employs scientific method and draws tentative conclusions based on the current most compelling evidence available and which are critiqued by a community of experts.
Naturalistic Pagans tend to be highly critical of the misuse of scientific theories to justify belief in non-scientific phenomena, something which is common among other Pagans. An example might be those invoke quantum physics or chaos theory to justify a belief in practical magic. While it is true that science has not yet proven all things which are true, it does not follow that all things which have not been proven by science are true. Most Naturalistic Pagans consider it acceptable social behavior, when a person makes a truth claim, to ask for their evidence and to subject the claim to a logical critique — even if the claim is a of a religious or spiritual nature. In this way, Naturalistic Pagans differs from many other Pagans, who may consider such behavior to be rude and insensitive. Recognizing this cultural difference in advance can help avoid conflict with other Pagans.
Science should not be confused with “scientism”. One form of scientism consists of overestimating the scope of the reach of science. An example of this is the mistaken belief that everything which is real is understood by science, and that if it is not understood by science, it must not be real. Another form of scientism is overestimating the reliability of scientific claims, taking as absolute truth what is actually only a high probability. Scientific theories, by their very nature, are always open to being disproved by future evidence. As Karl Popper has explained, science proceeds not by proving facts, but by disproving hypotheses.
It is probably true that not all questions can be answered by the scientific method. Many issues which concern Naturalistic Pagans may fall into this category. In these cases, humility is called for, not faith. The paucity of scientific evidence is not a justification to believe whatever one wants. In such cases, we must place the question in the category of the “as yet unknown” and suspend judgment. In the meantime, though, our condition of “unknowing” may be enriched by our individual subjective experiences. But we should remember that we can submit even our own experiences to the scientific method: experiment, observe, draw tentative conclusions, compare with others, and then repeat.
Naturalistic Paganism 
“An example might be those invoke quantum physics or chaos theory to justify a belief in practical magic.”
Considering thoughts/prayers, I can invoke quantum physics and chaos theory, but, such effects are minor and unpredictable. Rather, the main thing (if you make prayers at all, but even if you don’t, other thoughts) is it affects your own thoughts and state of mind, in order that if an action is needed to make the external effect, you may then do so.
“While it is true that science has not yet proven all things which are true, it does not follow that all things which have not been proven by science are true.”
I agree. Even, it is logically contradiction if all things which have not been proven by science are true.
“Science should not be confused with “scientism”. … As Karl Popper has explained, science proceeds not by proving facts, but by disproving hypotheses.”
Agreed. Only mathematics is you can make the absolutely proof; scientific doesn’t, but nevertheless is best way we have.