Second, you are in your rights to do those things. You can't discriminate based on race, age, gender or religion; tats, piercings and ugliness are fair game.
If you are in the US, CA or EU you should read up on what the local human rights/civil rights laws entail.
Edit: There are exemptions for "members only" places, which is different than public restaurants. but then you would no longer be a restaurant but considered a club. For example, the gym, curves, is members only. One of the membership requirements is being a woman. If they decide to open a coffeeshop on the side they wouldn't be allowed to have it open to the public. It's either fully open or mostly closed, now in between.
Really, when you think about it, not being a christian is a choice (which is why I didn't mention race, age, or gender). Just like this guy being an asshole.
It's not much different. Someone is getting excluded from business because another group doesn't like them.
Its called judging a man by the content of his character and/or skills. Its not discrimination. Someone with Parkinson's is unfit for a bomb disposal unit. Someone with arts degree is useless as Rocket scientist and useless at a NASA convention.
Having ill-considered opinions down voted isn't a violation of your right to free speech (which was never guaranteed in a private venue in the first place, by the by).
Instead, it's an expression of everyone else's speech. You're allowed to be wrong. Others are allowed to point it out.
So, if I start a restaurant and decide that only Christians can eat here, would that be okay with you? After all, non-Christians may tarnish the quality of the restaurant.
If I decide to not hire people with earrings, are ugly (let's say I have a hooters), or I just don't like, I would either get lawsuits for discrimination or from the ACLU.
How is this any different? and why shouldn't I also be able to choose whom I do business with?