Yes, it is a 9th amendment protected right, as an owner of private property, to refuse to sell or allow anyone for any reason onto my property.(skin color, hair color, gender, sexual orientation, religious orientation, lack of money, not dressed properly, not educated enough -- granted such discrimination may be bad for business, but that is up to the property owner to decide - free to choose, the essence of liberty)
Any compromise of this position is anti-liberty and muddles the important demarcation line between public and private property.
Government jurisdiction only exists on public property. Public property is taxpayer funded property: parks, schools, court houses, roads, firehouses, etc.
Not malls, restaurants, gas stations, homes, airplanes, country clubs, etc.