Only a matter of time until legislation squashes this....just so you know.
Sadly, there are plenty of legal precedents that would allow them to do so.
Right now, though, there would be nothing "illegal" about shipping them.
However, he should just vote with his checkbook, and take his business to a different shipper (his ENTIRE business)....(and take as many other gun-friendly businesses as he can with him)....
Then see if the carrier changes their tune....