They'll probably show you the door if you're shoeless or shirtless, too - as is their right. Get a mask, or don't go.
Yes I still believe a business has the right to refuse service to anyone. They were worried someone would turn them in to the state if I remain in their store. Like I said I had a mask on but it was not covering my nose in one store. The other I forgot my mask and pulled my shirt up over my nose and still was asked to leave which I did no skin off my nose pun intended.