It's your body and you can do what you want with it
HOWEVER
It's their company and they can set the rules as they want.
If a company feels it is detrimental or hurts their corporate image or branding I can totally agree with them not wanting/allowing tattoes in the workplace. Especially if you are forward facing and deal with customers, clients, representatives etc in a personal contact way,
What is tatooed is also a consideration. No matter how nice or talented someone is do you think someone sporting swastikas and kill all jews tattoed in visible, non covered up areas should be allowed ito work in most companies?
It can often times be simple discrimination, other times, it can be offensive to one group or subculture without even intending to be. It can oft-times be as simple as a company wanting to protect its name or reputation.
Remember, all it takes is one picture or meme or social media post by an employee, even off hours when not representing the company, to bring down the wrath of the public on that company.
Business' today have every right to ensure that their employees abide by that companies morals and ethical code of conduct (assuming all of this is explained prior to hiring of course)
This is why a lot more companies are including moral and ethics clauses, some even spelling out what can or can not be done with personal social media accounts, in their hiring contracts.
I have worked for a company in the past where I was not allowed to wear company logo clothing outside of the work place. They did not want to risk their company name being associated with anything negative. That was their prerogative and was explained to me prior to hiring. I agreed to that condition upon acceptance of their offer.
it's your body to do with as you will, but remember all actions have consequences and not everyone will look upon your actions as favourable.
You don't want people telling you what you can or cannnot do with your image, have the same respect for others when it comes to their image as well