Except for the lack of magic, I suppose?

I don't believe most educated, rational believers call their faith equivalent to a belief in magic, so that's kind of begging the question.

Anyway, if we start inventorying our personal beliefs and the rational, empirical basis for each of them, I think we all probably practice magical thinking to some extent.

I imagine some perfectly rational, omniscient alien interrogator questioning my most deeply held beliefs about, say, free will, or my individuality, or why the world is the way it is, and placing me somewhere on a continuum that includes witch-burners and cavemen, rather than in a completely separate category.

Depends, if a secular humanist believes that time, space and matter appeared out of nothing, which is indistinguishable from magic and on the grandest possible scale.

It's definitely less of a magical explanation than that everything was created by a magic personality of endless love and ruthless judgment, whom you know personally through auditory hallucinations and the writings on ancient scrolls.

Ok, but what about literally every other scale? Because those are the ones that matter re: morality and how we show up in the world.

Saying "both sides can't answer this one question" as though that implies that both sides are equally invested in magical thinking is a bit unfair.

A secular humanist probably defers to the physicists on that question and is fine with the answer "we don't know".

You would really have to stretch the definition of religion to breaking point to justify that comparison though. Secular humanism is fundamentally different in the way it was born, how it tenets are formulated and how it's practised compared to say to Islam or Christianity. Reducing both religion, as practised by billions of people, and a secular belief system to just philosophical systems does neither justice.

Secular humanists are fundamentally sceptical, whereas theists are fundamentally credulous ... is that how they are distinguished?

To clarify: sceptical in the sense of doubtful / needing to be convinced by compelling evidence, and credulous in the sense of being prepared to believe something with uncertain or only minimal evidence.

OP said secular humanism and religion were indistinguishable - my point is they are distinguished by their fundamental attitude to evidence.