Yes, they are not a government entity, however as a common carrier, they cannot refuse transport of legal goods without a compelling reason. "Guns are icky" is NOT a compelling reason. If it were HazMat and they did not have the capability to handle it, that would be acceptable. This is the law in the US.
These quotes were pulled from an old legal reference book my Great-Grandfather was issued as part of his duties at Consolidated Edison. A common carrier cannot refuse a shipment of legal goods unless there is a specific and tangible issue with the goods. (Declared value too high, not enough space, can't mix types of HazMat etc.) Once they decide to serve the public, they have to abide by a set of rules, those rules limit some of the "freedom to choose" / "right to refuse service" that they might otherwise enjoy as a contract carrier.
