ATHENS—When Katerina Dervenioti decided in 2013 to open a bar in central Athens, she was sure of one thing: there would be no smoking. She had always disliked it, and after all the government had passed a law banning smoking in interiors back in 2009.

It took only a few hours after opening her cafe in a trendy Athens neighborhood to be sure of a second thing: Greeks believe rules are meant to be broken.

Despite...