Each establishment will obviously have different policies which are enforced based on the people at the store.
That said, I won't patronize a chain which has an openly hostile stance against firearms, if I know about it. I just can't bring myself to do it. If the corporation gains financially by my patronage, and they actively discriminate against select civil liberties or "hot" topics, I won't be going in there.
Think of it this way: the corporation gains nothing by preventing access to anything, possibly with the exception of things like child porn. The only thing they will do is alienate people who want access to that material; people trying to access illegal material will say "oh well" and try elsewhere. It's basically a conscious "f*ck you" to people with those interests, whether legit or not. They offer "free" wifi to their customers, so they shouldn't discriminate. (Are they going to ban every jihadist web site? How about file sharing networks and sites like torrentspy.com? How about google.com, which assists people finding illegal, illicit, and otherwise "disagreeable" material?)
People find this behavior abhorrent from governments. It is. It should be equally abhorent from a "free agent" like a corporation which gains little to nothing by supporting such things. Unlike the government you live under, however, you've got much more choice in which companies you patronize. Keep that in mind...