The press actually does not have special privileges in the United States. Any citizen who is doing something that could be construed as journalism or reporting of news is protected by the First Amendment, not just persons who are professionally employed as members of the “formal press.”
Your post about discrimination and excluding blacks from a restaurant shows you know vanishingly little about American law, so in the future I really think you shouldn’t talk about it with such a definitive tone until you’ve done more research.
In the United States, business owners have the right to refuse service to anyone. This has nothing to do with the distinction between public businesses and private clubs, whatsoever. If I own a restaurant I can refuse service to anyone I choose based solely on the fact I think they’re ugly, I think they smell bad, I don’t like their hair style, I don’t like them because I know them on a personal level, because I don’t like their clothes, because they are too young, because they are too fat, because they are gay, because they are professional wrestlers, because they are convicted sex offenders, or because they are Civil War re-enactors.
In the United States any business which serves the public (essentially most businesses aside from entities which operate as private member clubs) has basically only one set of restrictions on the right to refuse service. Based on the legislation that came out of the civil rights movement, a business owner cannot refuse service to a person based on that person’s membership in a protected class. What this means is I do not have the right to refuse service to someone because they are black. Race is a protected class. I cannot refuse service to someone because they are Christian, religion is a protected class.
I don’t know all the protected classes by heart, but I know race, religion, and disability are the big ones. This is United States Federal Law, meaning there may be more protected classes in any of the fifty states, but the federal law’s protected classes apply in all 50 states.
What I do know is that sexual orientation is not a protected class. So barring any state law, I could prohibit homosexuals from eating in my restaurant, based solely on their sexual orientation.
Age is a protected class only if you are over a certain age, meaning I can’t prohibit granny from coming into my trendy night club just because she’s too old. However, the converse isn’t true. I can run a bakery and prohibit children from being brought in because I just don’t like kids.
Weight isn’t a protected class, so I can bar fat people.
Having a criminal history does not make you a member of a protected class, so any known convicted murderers, pedophiles et cetera I can bar from my establishment. (However there are laws about hiring procedures and whether or not you are allowed to use criminal history as a bar to employment, that is a different law separate from laws about who businesses must provide service to.)
Now, to address you hypothetical racist store owner who bars all blacks but does so under the technically legal excuse of “I don’t like that person” or “I don’t like their clothes” or whatever–that would result in a law suit. In the course of the suit if the aggrieved parties could demonstrate that the owner’s behavior was solely directed at blacks and et cetera, they could show that he was de facto refusing service to a protected class and he’d suffer the legal consequences (probably financial in nature in that case, not sure.)
While it should be obvious, being part of a protected class does not mean you can’t be refused service. If I’m black but also a known convicted murderer out on parole, a restaurant can refuse to serve me based on the fact that I’m a convicted murderer. They can’t refuse to serve me just because I’m black.
Finally, back to the press issue, a restaurant critic has no intrinsic “right” to be on a restaurateurs premises and to review their restaurant based on eating there. A journalist can write anything they want (within the bounds of certain laws about libel/slander etc) about a restaurant, and the L.A. Times has probably written negative articles about the restaurant in question. However, there is no special “critics privilege” which exists that says restaurant critics have a protected right to eat at any restaurant they choose. There is also no privilege that exists for any individual in America that says someone is prohibited from taking a picture of a journalist and publishing it on a website. There might be some privacy laws that would protect some people, but I don’t really know about that. If someone takes a picture of me on a public street I’m not sure what rights I have in regards to the dissemination of that photo. I would suppose if that photo was used in an advertising campaign, I could sue for use of my likeness in that regard. However if it was just posted on a non-profit website or something, or in a local newspaper, I’m not sure I’d have any leg to stand on legally.