Private discrimination is a different matter. I could keep black people, hispanic people, white people, blind left-handed people, or people who voted for Bush off of my private property simply because I wanted to. The government couldn't do anything about it.
A store may be private property but that doesn't mean that you can discriminate freely. I seem to recall during the civil rights era that blacks would enter restaurants or other businesses that refused to serve them and they eventually won. When you open a store to the public you are opening it to
all the public.
