Answer:
The First Amendment; freedom of religion, freedom of speech, freedom of the press, freedom to assemble, freedom to petition the government.
Freedom of Speech isn't exactly obligated in this sentence, but it's hard to come-by since it's a business' own employee.
The employee might have not intertwined his/her work industry within the comment, but when hiring someone, what are the best qualities needed? Kind, hard-working, selfless, helpful, and devoted, right? Unfortunately, a good way to get sales is to make your company look better. You don't want a racist guy, who people know works at your company, to be spreading their beliefs around like wildfire and racially discriminate people.
The employee may have Freedom of Speech, but that does NOT mean they can be protected by it in this situation. Rules are obligational to the Amendments. Like in school, when they told you to be quiet and you wouldn't, what'd you get? A punishment. Rules are obligational across every community that can walk, talk, think, read and write.
So my answer is no. As I stated above, rules are obligational, and whoever set those rules has right to punish whoever breaks those rules. Freedom of Speech can't help you in every situation.
