‘1A is not a privilege, it’s a right!’
it also does not apply to private property...
Private property as in one's home, you are absolutely correct. Public property whose function is to accommodate the public is another matter. Title II of the Civil Rights Act states: "42 U.S.C. §2000a (a)All persons shall be entitled to the full and equal enjoyment of the goods, services, facilities, privileges, advantages, and accommodations of any place of public accommodation, as defined in this section, without discrimination on the ground of race, color, religion, or national origin."
I believe in the case of a shopping mall or similar setting, the owner would need to show that he is denying service because the person is disruptive, drunk, disorderly etc. Saying that someone wearing a Jesus shirt is a threat - would be a stretch in any courtroom - IMHO.