Since time immemorial, perhaps since prehistoric times, religion and politics have been tightly twisted together. And still today! Religion has been enormously useful for politicians to do stuff they wanted that had nothing to do with religion. It's been used to justify wars, genocide, slavery, you name it.
That's what's happening here. The American fundamentalist Christian movement has been co-opted by the Republican Party. Otherwise intelligent, well-meaning Christians don't understand where religion leaves off and politics begins. They've been sold a political bill of goods as religious tenets.
And they've been carefully taught to believe their rights are being abridged, their 'religious freedom' is under attack. Because anger, wanting to fight for your rights, is a big political motivator. It gets people to the polls.
This is why Christians believe gays and Muslims and blacks and Jews and Muslims are 'taking over'. It's why they believe THEY should be the arbiters of our national morals, why they see this as their right and just 'the way things oughtta be'. It's why they keep picking fights over baking cakes for gay weddings, etc.
Refusing to serve Christians is the same as refusing to serve gays. It's not protected by the 1st Amendment, in fact it's the 1st Amendment that makes it illegal!