I'd say no, tattoo's are a form of expression, and so is hooping.
However if you get a tattoo, it's gonna limit your performance abilities for a while.
I got a tattoo covered up recently, and the new one is quite a good size but it's on my hip, so i've been practicing alot of isolations and off body hooping.
Maybe? I think it depends on the tattoos and the clients. But luckily you get to create you costumes so there's no reason you could where sleeve to over any arm tattoos, you can even get sleeves that are skin colour and then wear a little arm band at your wrist so it looks more natural. It might take some time to get used to hooping with fabric on your arms and to not overheat but over time you would get used to it.