Can you sue a fast food restaurant for kicking you out?
In the US, if they kicked you out due to your status as a protected class member (race, gender, religion, national origin, some others in other states), that is illegal and you can sue them. So if you're Arabic, and they told you "We don't serve terrorists here", yes, that's illegal racial and/or religious discrimination that they would be liable for.
If you can't demonstrate it was for one of those reasons, no. If you were causing trouble, or they thought a slogan on your shirt was offensive, or for whatever other reason they decided they didn't want you there, they can throw you out. Unless you can demonstrate it was protected class discrimination, it's their property, and they can kick you off of it if they so choose. Most businesses don't just do that arbitrarily, or they don't tend to stay in business too long.