I wonder if it will ever get to the point where a company can say a condition of employment is no gun ownership? On one hand they can say you don't HAVE to work there. On the other, is it legal to deny an employee a constitutional right on his private time?
I don't know if its correct or legal, but companies have fired employees because of social media comments. Nothing adjudicated in court.
In Oklahoma and other states, it's a fire at will with a few caveats. Not sure if this is all of them but organizing a union, discrimination, and maybe others will get you a pass.
Otherwise you can be canned without any reason.
Unless it's affecting a protected class, a company can make pretty much any rule it wants for employees, particularly in an at-will state. You have to understand, the company isn't "denying [the] employee a constitutional right;" only a government can do that. The company is entering into a contract with the employee that says "in exchange for employment, you agree to these conditions." "Morals clauses" are common among public figures, but can certainly be added to any contract. Those terms can include foregoing the exercise of something you otherwise have the right to do; it's called a "forebearance," and it's not only legal, it can in some cases be one of the elements necessary to form a contract ("consideration," that is, that the parties each give something to the other). Hamer v. Sidway is the case in pretty much every contract law textbook.