Perhaps this is not the case in your nation, but here in America, they are most certainly not professional. I don't set the standards, but I wish to operate in a professional setting, so I abide by them. There's also the fact that they're inextricably linked with crime and prisons, and I would never wish to be seen as associated with such things.

I think they probably mean "they're taboo, which can sometimes be construed as unprofessional".

Tattoos don't stop you from acting professionally but let's not pretend that a presidential candidate could have a face / neck tattoo that wouldn't dominate the news cycles and activate the purity police.