Restaurants and stores qualify as “public accommodations” even if they’re a private business. As such, discrimination laws apply just as much on private property and to private businesses as they do in any public place.
Whether you post a sign or not, businesses never have the right to refuse or turn away customers because of their race, gender, age, nationality or religion.
Most ranges require membership for use. Meaning, they are Private, not public.
Does not equate.