Personally I would never exclude someone based on visible tattoos. We are in a creative industry, expecting the designers not to be creative seems like a bad idea. Personally I don’t have any tattoos, mainly because I am fickle and I can’t imagine having to choose… and I’m also a whip, combine those two things and no tattoos. 
Also really good tattoos are expensive and I’d rather spend my cash on horsepower… I digress, so while I don’t mind it to the point that I just don’t care… it really seems to bother some people and I could see some employers not allowing it. My wife works for a hospital with strict no visible tattoos rule. Since they can’t discriminate based on appearance, those with visible tattoos have to cover them. So one of her co-workes that has a full sleeve has to wear a full compression type arm thing to cover them while at work. Same place once allows 1 piercing in each ear, but my wife has 4 piercings in each so she has to take them out every day. I think it is totally stupid, but those are there rules. As long as you are comfortable with electing to deal with that, it’s your call.