If he can't do it when working with fast moving machinery, they're asking him to put himself at unnecessary risk which is dodgy to say the least. Surely health and safety outweighs appearances in this case?
Also, if there's nothing in the contract, and nothing said prior, can he not just continue regardless? Would there not be ramifications for dismissing somebody on those grounds?
I'm on the side of the mechanic here, wouldn't bother me if it was my car, shame that people still find this a problem. Let it be a warning to those who are thinking about getting tattoos to think twice about it. Not least because they usually look awful in my opinion.