Yeah I know. Totally expressing your political idealism in public should be punished! Woot!
While it was within their rights to do, less they were causing a scene it's pretty stupid. And I don't applaud stupid.
Legally a person's personal property is not a public place, you don't have the right to be there doing anything if the owner doesn't want you to. Of course there are certain restrictions on an owner's right to remove someone from their establishment, for example an owner wouldn't have the right to remove someone for being black. However when you are disturbing other customers, and disturbing business, and when the owner has specifically asked you to leave, that's trespassing.
Its just like the police officer says in the video, when the owner tells the man "I will not serve you, you need to leave, you're trespassing." The guy looks at the cop and the cop flat out says, "Sir, you are
going to trespass you need to leave." He says going to trespass because he's giving the guy an opportunity to leave, after all he's not trespassing until he's told he's trespassing by the owner. Given the nature of the establishment which is a coffee shop, a reasonable person can assume entrance is permitted without prior approval. It would be different if he jumped a fence covered with signs that said no trespassing. So anyway, now that the officer has informed him that he's going to trespass if he doesn't leave, the man is legally obligated to do so in respects to the property rights of the owner.
I also believe the law requires an opportunity to leave after being informed of a trespass in situations like these where entrance is permitted without approval or entrance is revoked after the party has already entered. Otherwise once the owner said you're trespassing, the officer would have had to arrest him on the spot which wouldn't have been right because there would be no way out for that person to not trespass. (He can't very well instantly teleport himself outside can he)
So in the end a bunch of loud mouths went into a coffee shop, which is a place a reasonable person can assume they are allowed entrance during business hours without prior approval by the owner. Then they started making a disturbance, the owner decided to remove them, once they were informed they had to leave by both the owner and the police officer, they left.
Again, I don't see the issue.