CLEMSON, S.C. — Pete Matsko expected a little pushback when he posted a sarcastic sign banning concealed weapons from Backstreets Pub & Grill, his beer and burger bar in this college town, but he did not expect to become a national target.

Within weeks, he was slammed with so many online attacks and harassing phone calls that he changed his number and started asking the police to open his mail.

A new concealed-weapons law in South Carolina turned his pub into a battlefield in America’s culture wars. Like an increasing number of bar and restaurant owners around the country, Mr. Matsko discovered that his politics can matter more than what he serves.

As the position restaurants hold in American culture grows, so too does the list of issues on which chefs are asked to make a stand. Refusing to bake a cake for a gay wedding, requesting that a woman not breast-feed at the table or trying to prevent a diner from wearing a gun can have serious business implications.