Can I sue the restaurant for rude customer service?

You can sue anyone for almost anything but that does not mean you will win the lawsuit or have a case. You have absolutely no case here. You should not have ripped up the bill and he should not have been rude to you but neither ids a crime or a civil tort. If he threatened you that is harassment. If he told you to leave and you did not that is trespass on your part. If he asks you not to come back and you do that is also trespass. The owner is not going to care and he will probably side with the manager. All you can do is not go there anymore and be more patient and kind to people in the future and hope they are patient and kind to you. The minute you get in someone's face they are going to ber ude and insulting and shout at you as that is the way most people are today. They will not tolerate abusive people in their businesses and they will have you arrested or throw you out. I was not there to see who was rude forts or who asid what but I would advise you that if you are someone's place of business and make a scene they are going to call the police and it is likely to be you that gets arrested for Disorderly Conduct, Trespass, and maybe Resisting Arrest or Obstruction.

With respect, one doesn't sue for rudeness at an eatery. Choose to go elsewhere in the future, certainly. Encourage your friends to not visit the place, can see that. In the FWIW category, it is rather unusual to rip up a check into individual orders. It is far more common to request separate checks if there is a need or desire to pay individually.