I don't believe, for example, that the universe was deliberately created by anything remotely person-like, nor that any such entity (supposing I were wrong about that first belief) shares in any singular sense identity with whatever entity or entities provided to early Jews the laws and tribal history currently known as the Torah, nor that those entities have any relationship worth mentioning to do with what happens to me upon my death.

If (as I suspect) you consider Judaism to be contingent on those beliefs, you would conclude that I'm not Jewish

More specifically, what I would conclude is that your self-identification as "Jewish" (rather than "of Jewish parentage") is a misguided effort to continue affiliating with a tribe that you're used to belonging to, but that you would never have joined in the first place had you had your current beliefs at the time of joining and had you been taking them into account in deciding which tribe to join; and if, for example, it turned out that you were avoiding the use of electric lights on Saturdays, I would have no hesitation in labeling such behavior as irrational, even silly -- and I would be entirely unsympathetic to the extent I viewed the behavior as a tribal affiliation signal rather than, say, a psychological compulsion (which I can understand and relate to).

I am in no sense a Canadian, for example, but I'm not sure I'd be mistaken if I respond to expressed disrespect of Canadian cultural icons as though it were my culture being disrespected (for example, by being offended on their behalf).

In all honesty, I would tend to view that with suspicion also -- my instinctive perception would be of an obsequious attempt to curry favor with Canadians. This perception could be overridden, of course, depending on the circumstances; but I would sympathize with disapproval on the part of a non-Canadian more than offense per se.