A shop can turf you out for any reason. It is private property and you are in it at the owner’s pleasure. No reason needs to be given. How that pans out for civil rights is that the owner can then be sued for civil rights violation if it can be proven that it was a civil rights issue and not a personal objection to the customer.
The store owners civil rights are protected as well by law and this extends to being allowed to decline to serve any customer but with the above proviso and which must first be expounded upon and then proven. It is not even a matter of religious liberty.
Some people find homosexuality disgusting without any religious underpinning for their reaction. This is a natural reaction to a perverse and unnatural act. That is why it has been illegal and even punishable by death for most of human history. This current phase of history is not even human.