Yeah this is just completely untrue. A business owner can refuse to serve you for any reason, as long as it isn't a specifically protected reason. Much as a company can fire you for any reason except for the legally protected ones.
Actually, a restaurant can ban you for anything outside of specific protected classes like race, gender, religion. A restaurant can ban you for your political beliefs, who your friends are as long as they are not a protected class, they don't like the breed of dog you have, or anything else. Welcome to a free country.