Nobody talks about users of dishwashers, or users of retail stores, or users of telephones. So why are we talking about “users” of computers, browsers, and software?
To me, the term “library user” always had the stink of questionable doings at the library. “Library patron” sounds too removed from the innocuous use of library resources. I don’t have a better term (“customer” makes me gag), but “Library denizen” has some zing to it, don’t you think?