Let me say up front that I think the article's headline is a bit of a stretch.
To play devil's advocate, though, you don't have to look back too long to find a time when anti-Semitism, for example, was so passively widespread, was so much a part of standard liberal intellectualism, that one could even argue that there were people of no particular malice who would exercise discrimination against Jews. It wasn't any sort of burning hatred, just so much that "everybody knew" that Jews couldn't be trusted, or would bilk your money, or scare your good Christian babies, or whatever... (For those that believe this sort of faddish anti-Semitism still goes on...well, you won't find my arguing the other side.)
The point is that the prevalence of "No Jews" signs could be seen for a lot of the 19th and 20th centuries as a passive and pervasiveness ignorance. The fact that such a level of ignorance was (and still is) profoundly insulting to those on the receiving end of it is very important, but it still represents something different from, say, cross-burnings and lynchings in the spectrum of bigotry.
Taken in that light, the analogy isn't indefensible; the notion is that all those anti-gun businesses are following the passive prejudice induced by the fact that "everybody just knows" how dangerous guns are and therefore shouldn't be brought around right-thinking people.
It is a form of prejudice induced by pervasive lazy thinking and ignorance (sometimes willful ignorance) surrounding legally owned firearms. And, as with past incarnations of such ignorance, patient education is probably the best long-term answer.