Magic is so notoriously vague and undefinable that it is a relatively useless concept. (Experts tend to agree.)1 This is relevant because it renders the charge that theistic explanation is “magic” a fairly meaningless one. By contrast, “theistic explanation” (and “supernatural”) do have relatively clean definitions.2
Magical explanations are sooner defined as a special kind of natural explanation (a weird or hidden part of it).1 This is relevant because theistic explanations are quintessentially supernatural explanations (not natural).
Explanations with no mechanism are just appeals to magic. This is relevant because theistic explanations lack a mechanism.
• …it implies fundamental particles (w/ interactions) appeal to magic.1
• …non-magic “Personal explanation” can lack explanatory mechanisms.2
• …magic often works through mechanisms (magical ones).
• …magic is a useless concept (notoriously undefinable)
• …personal choice is arguably a mechanism.3
• J. P. Moreland: “A personal explanation can be epistemically successful without referring to a mechanism or other means by which the hypothesized agent brought about the state of affairs in the explanandum. I can explain the existence and precise nature of a certain arrangement of objects on our dinner table by saying that my wife brought it about so we could have an Italian dinner with the Isslers. That explanation is informative (I can tell it's Italian food we’re having, that we are having the Isslers over and not the Duncans, that my wife did this and not my daughter, that natural processes are inadequate). In addition, the adequcy of such a personal explanation is quite independent of whether or not I know exactly how my wife did it.” [Consciousness and the Existence of God: A Theistic Argument (Routledge, 2008), 105.] And yet personal explanation is not “magical,” whatever that means.
Explanations citing supernatural entities or events (i.e. beyond nature) are appeals to magic. This is relevant because theistic explanations appeal to the supernatural.