No, a private entity can refuse you service for any reason they want, except for a few protected reasons. You can refuse service to someone for the attitude, offensive clothing, or because you don't like their face. But you can't do it because you don't like their skin color or sexual orientation. There are some exceptions carved out for religious views, like in the case of sexual orientation, but even the church can't kick you out for your skin color. So it's a hybrid of religious exceptions, and private entities can be selective