. . . If your point is to claim that magic is associated with religion (understood to cover the widest possible range of practices and beliefs, not limited to the “world religions”), then yes, you are correct. This is a fairly trivial finding. The problem arises, in my view, when magic is applied indiscriminately, because one may wind up in a situation in which all thought is construable as magical thinking. I have a more restricted understanding of magic as a “technique” (for definitions, I’m persuaded by the Maussian/Durkheimian line that focuses on the “form” of religion versus that of magic) as opposed to magical “ideas” or beliefs. To be sure, a practitioner or adherent likely believes in magic as a technique, that it works, just as the sinner believes confession has some impact on the disposition of her soul and the patient believes the medicine administered by the physician is having a physical effect (I’ll leave aside the problem of placebos). Where the ideal-typical rationalist parts company with the ideal-typical adherent of magic is over the method of confirmation; the experimental (or some approximation of this) method that enhances the experience of reality beyond that captured by the senses (rationalist) versus a heightening of the powers of phantasy, which allows the magician to manipulate unseen forces (adherent of magic).

And why shouldn’t the animist’s belief in spirits be put into the same box as “belief in things which contradict logic or known physics”?

Yes and no. As form, a form of thinking, and as a method of confirmation, the belief in a spirit world is incompatible with “known physics.” For the former, the world is ordered like an order of thoughts, and hence, thought or imagination (phantasy) offers access to this world. For the latter, the world is ordered by empirical laws which exist outside the mind but which can be brought to mind through experimental techniques as opposed to phantasy or introspection.

However, from another perspective, the animist and the physicist share a common belief that there is an order of experience, that experience is ordered, and that thought can comprehend this order. Or rather, that this order can be represented in the form of ideas. This belief is what they share insofar as science and animism are defined as forms of thought.

“Magic” is what they practice at Hogwarts.

Forget “muggles science”; contrast it to Giordano Bruno. According to Ioan Culianu:

Of the categories of magic in the Renaissance, the most interesting is undoubtedly that of Giordano Bruno. He lists nine categories: sapientia, magia naturalis (medicina, chymia), praestigiatoria, a second form of natural magic, mathematica or occulta philosophia, a magia desperatorum, which is demonomagic, also called transnaturalis seu metaphysica or theourgia, necromantia, maleficium (of which veneficium is a subcategory) and divinatioor phophetia (De Magia, III, pp. 397-400). Eros and Magic in the Renaissance, 170.

Bruno is one exemplar of range of material included in Renaissance “science.”

If I have a category of “things not compatible with logic or known physics”, why isn’t a good name for that category “magic”

It depends on one’s point of view. If those incompatible things include that which is unknown, then it would matter whether one thinks the unknown falls in the category of the not yet known by physics or in the category of the unknowable by physics. Would the former, the “not yet known,” which at the present moment is “not compatible” with “known” physics, lie in the realm of magic?