I don’t know who or what store you are referring to but I find your statements disturbing. Since you already judged him as nonreligious for keeping a business open on shabbos (which you seem to be the only one that knows that there is a Jewish sole-proprietor) you refuse to accept any reasoning that the actions of the owner may actually be permissible.
I don’t deny that there are individuals that keep mezuzah and daven but are mechallel shabbos. I don’t consider them frum but they aren’t just putting on a show.