Remains to be seen. I would like to see a legal challenge. Places of public accommodation should be forced to abide by the laws of the community in which they do business. If open carry is the law in that state, a business shouldn’t be allowed to deny access to someone who is acting within the law.
Most states allow businesses to prohibit firearms on their premises. But most have specific laws about what must be posted and where to prohibit carrying a firearm.
Privare property can tell you no guns or ccw only.