It's the store owner's prerogative to not let people with covered faces in their store.
It's not that simple. Who will deal with accusations of racism and/or Islamophobia?
The store owner will. He puts up a sign that says "No face coverings of any kind permitted in the store". If some Muslims want to accuse him of Islamophobia that's their right, and it's the store owner's right to defend himself from the charges, and his customers will decide who's right. Yes, there's a chance his business will suffer, but there's also a chance it will do better if people flock to his store in defiance of radical Islam/political correctness. The publicity could work for him and he could pick up some valuable allies to help defend him from the charges of racism and Islamophobia.
But for the better or worse, that's how a free society works. I certainly wouldn't want some nanny-state passing face-covering bans to insulate private businesses from criticism. People have the right to dress how they want for religious purposes as long as it does not infringe on someone else's rights (in this case, the business owner's right to keep his jewelry store secure), and people also have the right to make any ridiculous accusations they want.