As someone who has a co-worker with a full sleeve, I don't personally care. However my district requires that tattoos be covered.

As far as the legal ramifications of it, as mentioned below, it surprises me that nobody has pushed the issue yet. Tinker v. DesMoines (1969) states that just because a student or teacher step foot on school grounds their 1st amendment rights do not stop. Therefore speech (as discussed in regards to clothing, but could extend to tattoos in my opinion) cannot be stopped unless it causes a classroom disruption. In my band-director-knows-everything mind, I believe that requiring teachers to cover non-vulgar tattoos is a violation of the Tinker v. DesMoines ruling and therefore illegal. But given that I have no tattoos that would normally be visible nor do I have the capital to fund a fight all the way to SCOTUS, I'm not pushing the issue.