"I support free speech, but I don't have to provide a platform for it"

Imagine that there was a restaurant with a sign on the window saying "no blacks allowed". And, indeed, the restaurant owner refuses service to black people and demands them to leave the premises if they attempted to enter.

When questioned, the restaurant owner states:

"I fully support equal rights for all people, and I also fully support anti-discrimination laws, and I'm strongly against racial discrimination. It's just that I don't have to provide service for black people in my private property. Just because I support their rights doesn't mean I have to like them, or provide them any services within my property. This is not away from their rights nor any services. There are literally dozens of other restaurants and shops within a mile radius of here which they can freely use. Me doing this does not stop them from going somewhere else and using their services. It's only racial discrimination if the government does it; it doesn't apply to private citizens nor their private property."

I think you would agree that that would never fly. Not only is the guy a huge hypocrite and an asshole, but he is, in fact, discriminating against people based on race and thus is for such discrimination, even when he claims he isn't. His actions speak louder than his words. His hypocrisy and racial discrimination would be rightly criticized.

So, given that, why should it be different if we change that to free speech?

"I fully support free speech for all people, and I'm strongly against government censorship. It's just that I don't have to provide a platform for people to express any opinion I disagree with and I don't like. Just because I support free speech doesn't mean I have to like it, or provide a platform for it within my service. This is not away from their rights. There are literally dozens of other platforms they can use to express their views. Me doing this does not stop them from doing it somewhere else. It's only censorship if the government does it; it doesn't apply to private citizens nor their privately owned services."

Why would that be any more justifiable?

I don't think it is. If you say that you support free speech, but at the same time you are providing a public service and forum for the public to express themselves, but deny access to those with the "wrong" opinions, because you don't like those opinions, then you are a hypocrite, and you do not really support free speech.