I don't think Free Speech has ever meant being required to publish others speech. Freedom of the press was meant to ensure you can say what you wish via pamphlets or starting your own newspaper, wherein you own the method of speech. That is why it was fundamental to Free Speech.
One has never been able to compel a publisher to publish them.
You may have a different concept, but to my way way of thinking that has always been the connection between the First Amendment and Free Speech.
But, since you asked, businesses that offer services to the public can refuse service to anyone UNLESS they're refusing a member of a protected class, for being a member of a protected class.
White restaurant owner kicking out a black lady because she's belligerent/drunk/whatever -- fine.
White restaurant owner kicking out a black lady because she's black -- not fine.
Religious bakery owner refusing service because it's Monday -- fine.
Religious bakery owner refusing service because the customer is gay -- not fine.
One has never been able to compel a publisher to publish them.
You may have a different concept, but to my way way of thinking that has always been the connection between the First Amendment and Free Speech.