Let's say that the employer does not choose to employ Jewish folks, or ones whose skin is darker than his own.
Like, for example, the Catholic Arch Diocese of New York, or Steven Spielberg casting Nazis in "Schindler's List"?
I do not believe the Constitution grants the Government the authority to regulate who a private citizen hires or associates with, nor to support members of a particular sect or race; it forbids the Government from doing so. By extension, the Government cannot contract out to businesses which have such practices.
Of course, I am also free to not seek employment with or to patronize businesses with bigoted practices. I'll decide if some store deserves my money, and thank the Govt. to stay out of it.