If I was trying to portray a professional image to clients that were going to trust me with significant assets or important business stuff, I would not send out people with visible tattoos to do client interaction.
If I was in the business of training combat skills, I would search out people with specific backgrounds that often include very specific tattoos. These would probably end up my most trusted employees/instructors.
Different standards of dress and appearance apply based on the job requirements. I know that I certainly would not do financial business with someone wearing tattoos that are gang or prison related, or using symbols associated with various hate groups. They might be the nicest person in the world but I would not be able to trust them and would not risk the future of my family on that particular gamble. For me personally it is about managing risk. For a company managing their image, it's the same thing. Why should they risk their image and the loss of a client by presenting an image that doesn't exude "trust me I'm good at this"? Sorry, but in "that world", a full sleeve tattoo doesn't give an immediate impression of business competence. There would have to be additional proof there somewhere, and establishing competence in the face of a bad first impression is an uphill battle.
A nice kid and his girlfriend were eating dinner next to us, and I noticed he had some gang/prison/hate group tats on his hands and neck. It was a small place so I couldn't help hearing his conversation, and he sounded like a really nice guy. But I sure wouldn't let him anywhere near my wife and kids. Maybe he's reformed, maybe he got the tats to survive in prison as he paid for a mistake, but just maybe he's a psychopath who would assault me or my wife because we are a "mixed race" couple. He will never get a chance to prove anything to me, and I stayed between him and my wife until we left. The tats were the only thing that made me think that way. I'm normally very tolerant (grew up in San Diego, so yea, tolerance) but a potential threat is a threat, period.
Like the dental assistant who had a bumper sticker of "the shocker" on his car. Does anyone really think I would be comfortable letting a guy who proudly displays a sex act on his car put his hands in my mouth, or in the mouth of my wife/kids, possibly under sedation? That guy won't EVER be near my wife/kids and I'll refuse treatment if he's the guy assigned to me during my next dental checkup. He probably has the same design tattooed somewhere because its that important to him. Fine, he gets an official workplace harassment complaint and I don't trust him to do his primary job with me or my family.
So, yea... Tattoos DO matter. Some more than others, and more to some people than others. If that is the image you want to present to the world and you're fine with the consequences, then go ahead get all the tats you want. Just don't complain when the consequences happen.