This is a difficult question.
With the exception of military veterans, I would have to say that most older teachers, (such as myself), do not have tattoos. The concept of body piercings and tattoos is largely foreign to teachers of my age group.
The reality is that the world we live in today is not the world we began teaching in 20-25 years ago. Our culture has changed and more young people such as yourself, now sport one or more body ornaments.
The question you have posed is being dealt with at the district level vis à vi revised faculty dress codes.
Some school districts are clearly more permissive than others. In general, I would say that discretion is the rule of the day. A discrete tattoo on the ankle or arm is quite different from a person who comes to a job interview literally covered from head to toe in garish tattoos.
In general, I think school districts as a whole tend to be fairly conservative ... so social mores that may be permissible outside the workplace are sometimes deemed unacceptable at work. Not only is this true for public and private school systems but it's also true for the private sector as well.
You may want to read the following article that was published by USA Today.
Schools enforce dress codes — for teachers