Telling a black man that he may not work in your bank because he is black is in reality a very different thing from telling a gay couple that you’d be happy to sell them cupcakes or cookies or pecan pies but you do not bake cakes for same-sex weddings — however much the principle of the thing may seem superficially similar. If the public sphere is infinite, then the private sphere does not exist, and neither does private life. Having a bakery with doors open to the public does not make your business, contra Justice Harlan, an agent of the state. A bakery is not the Commerce Department or the local public high school.
A relevant precedent mentioned in the story is Wickard v. Filburn. Farmer Filburn was minding his own business, growing wheat on his farm for private use, when the government told him he violated a government crop support program. Thus, somehow, since everything is "public" action since it affects commerce and policy everywhere, there's no room for "private" action.