Believe it or not, a private business may have an easier time doing this than many religious organizations. If a business is set up as a partnership or a closed corporation (i.e., it is not publicly traded) and its religious identity is written into its bylaws, it actually has a very strong leg to stand on in a legal case. This is why Hobby Lobby was successful in their ObamaCare appeal, while many religious organizations that get tons of government funding were not.
People need to learn this lesson - If you dance with the devil you get burnt.
Once you ingest the politicians poison, the principalities in high places gain control of your soul. (Evil has to be invited in)
And I bet a lot of conservative, christian owned businesses will be changing their bylaws to add religious identity.