No. Religion, race, sex and national origin are protected classes under the Civil Rights Act of 1964. (Sexual orientation is not protected under federal law, but is under the laws of some states.)
A business couldn’t legally ban Christians, but the Civil Rights Act of 1964 is clearly unconstitutional. The government can’t amend the constitution via law, and those class protections restrain government, not citizens. The 14th Amendment extended those protections to states (state governments), but again, nowhere in the constitution does it say I can’t discriminate on the basis of sex, race, or religion so long as I’m not acting in government capacity, like an official.
If I’m wrong, please point me to the area of the constitution that limits my right to associate or not associate with whoever I want.