public accomodation means you need to treat everyone the same way, /regardless/ of race, class, etc. This is the opposite of what you seem to want it to mean.

Exactly, in a free society you are free to discriminate. If you want to be a racist bigot you are free to do so. You're saying if you have a business your accommodating the public. What im saying is a business is your business its your private property and you are choosing to use your labor and your capital to engage in exchange with other individuals. If you then force me to serve someone that I do not want to then you're infringing on my property rights and forcing me to associate with someone I do not wish to. Whether I have a store-front or not it should not be relevant it is my property that I am willing to engage in voluntary exchange with other individuals. This of course goes with economic liberty which is the base im working off of. You're currently basing your argument with the notion that government has any right to regulate the exchange of goods between individuals which is a false assumption probably rooted in the commerce clause which from a constitutional pov is wrong (but has been interpreted that way by activist judges and authoritarian presidents) and from a philosophical level of the role of government in a free society should be soundly rejected otherwise you get our system of crony capitalism.

So you do not entirely have free speech - you can be held accountable for the impact of that speech.

Only if its your intention. I can't find the case right now since the Chicago Trump rally fills up the google search I would usually use to find it, but there was a case in Chicago I think in the 50s where some communist was giving a speech. The people got angry and the police asked him to stop his speech. He refused and was arrested. The court then ruled he could not be held responsible for the damage caused by the rioters simply because his speech caused harmed because he had no malicious intent.

Not to mention as I stated before liberty means being able to do whatever you want as long as you don't harm others. If you directly cause harm to others intentionally of course you can be held liable, but refusing service to others doesn't do that.