We'll start with the PS first....I'm aware.
I understand you didn't intend it to come off as it did and that you tried to "undo" it by the sentence you point out.
Here's the thing, I don't necessarily beleive any soul belongs to any specific religion either. However, as you should know, seeing as you love to explain things to people so much, sometimes words aren't an exact relfection of one's feelings. It's difficult to distill my atraction to Judiasm in a few words or sentences (some of it likely has to do with Jewish ancestry in my line that I was unaware of, but I can't explain the rest). However, when one writes for a living, words are the only tools we have. Given I'm writing a relatively short article in response to a prompt and not a treatise on my spiritual journey, I opted to keep it short and "athiest with a Jewish soul" is about as accurate as I can get within those parameters.