You can name this Freedom of Conscience and make attempts to allude it somehow holds up the First Amendment Rights, just like you can call a duck a cow. However, I believe if it walks like a duck, quacks like a duck, looks and smells like a duck...it’s a duck!
What it truly means is the right to deny civil liberties or human rights to others based upon your religious beliefs! The “right” not to provide medical services, such as abortion or sterilization procedures, because doing so would be contrary to the individual’s religious beliefs or moral convictions. The right not to provide services, such as baking a cake, because the couples’ gender preferences are not in your religious wheelhouse. The right to not issue marriage licenses to a same sex couple, because of your religious beliefs. The right to endorse and fund raise for candidates through the church because that candidate lines up with church ideals...all while maintaining tax-exempt status.
Some of my Christian friends are peeing your pants right now, because this sounds so good, right? Right!!! Will it sound good to you when the Hindu grocery clerk refuses to allow you to buy the sirloin steaks you picked up for dinner? Or the Jewish person in the quick-care waiting room turns off the TV everyone is watching because it’s Saturday morning and it’s Shabbat. Are you good with every child in the Second Grade classroom sitting through the Pledge of Allegiance because the teacher happens to be a Jehovah’s Witness? These examples are of other major religions. I could share examples of minor religious groups and cults, too. Some that believe in mutilating genitalia, in polygamy, in covering women from head to toe and gang raping her for minor indiscretions...enough said.
Bottom line, there is a very clear intelligent reason our forefathers kept Religion and State separate. We are NOT a Christian nation. We have many faiths and for some, none at all. Our laws protect all the people, not just the ones your religion picks and chooses.