I would be interested in hearing from FU BeAR on how mask wearing ordinances violate the fine citizens of Georgia’s rights under the US Constitution.
Globally speaking, any imposition by the government on freedoms to do what you want is an infringement on liberties. In many instances, the government can demonstrate that the benefits of the burden outweighs the infringement.
I think there's a perfectly fine argument that the imposition of a mask law is not a burdensome imposition on your liberties such that it would be unconstitutional.
Georgia's current issue is two fold:
First, the governor has issued a series of executive orders "protecting Georgians." In one of those orders he "strongly encourages" Georgians to wear masks. How can you put in an order that you "strongly encourage" someone to do something, you might ask. I have no idea. But that's what he did.
The order also provided that local municipalities could not impose rules stricter than the government did. Many local governments looked at the obvious ambiguity - you "encourage" me to wear masks, didn't order me to, but didn't order me not to. So they passed mask ordinances in several large cities (Savannah, Atlanta, Athens among them).
Second, the governor issued a new order two days ago that has the same "strongly encouraged" language from the prior order, but now prohibits local municipalities from ordering masks. Essentially, closing the loop hole.
What's peculiar is that the governor consistently argues that everyone should wear masks. He just won't require them to do it.
The annoyance of many in Georgia is that the governor has now put up a blockade to local government's doing what they need to do on the ground to protect their citizens. What makes Georgia an outlier is both that the governor has not ordered masks mandatory, but also prohibited local municipalities from making them mandatory in their own communities.