Meh.
Its been 200 years since ANYBODY knew how to make a tattoo.
First you need ink.... then a machine.. meh... to hard to do.
I dont think even RAIDERS have tatts.
And this is DIVERGENCE. In the 40s 50s, people were more moraly uptight.....
Really? Do you think people who tattoo in a federal prison have all the real equipment? No, they've got ink and a needle, it usually get's infected, but it's not that difficult to do without all the right gear, there is no sensible reason why tattoos would be any problem to make in the Fallout universe.