A company whose employees deal directly with the public has every right to establish reasonable appearance standards.
What it doesnt have the right to do...is to enforce those standards arbitrarily and retroactively. If they hired you as a driver in '86 with a Navy tattoo on your forearm, they dont have the right to come back 27 years later and say you have to start covering it. By the same token, if you have made a personal choice to tattoo flaming naked big titty biker chicks with skulls and swastikas on your arms, you cant get all butt-hurt when the company orders you to cover that crap up.
Tattoos are becoming more and more socially acceptable as time goes on. Ideally, the company and the union would sit down together and establish general guidelines as to what sorts of tattoos are and are not suitable for public view. Case-by-case decisions as to the suitability of a particular tattoo would be made by a committee at each building composed of an equal number of management and hourly employees. I think that if both sides were reasonable and respectful of one anothers viewpoints, it could work. Simply forcing all employees to cover all tattoos is not reasonable; neither is allowing each employee to ink himself in whatever manner he sees fit regardless of how offensive his choices might be.