Nope,..... private can not discriminate on race, religion or sex.
For the record too Climate Deniers web sites and a Fox News is next.
Sorry you are just wrong.
“Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.”
Do you see “Apple” or “Facebook” or “A private company”?