Tattoos are a fashion item, indulged in by people who have failed to appreciate that fashions change but tattoos are permanent! Such a lack of forethought and judgement could be reasonably penalised at interview, don't you think? You might say 'I was young, guv, and didn't understand the consequences', but, as BEags implies, I can find several equally young people who did understand the consequences and thus whose judgement I might consider to be somewhat more sound - a quality I value more than a little in a pilot.
Of course, if your tattoo is small, tasteful, and not in view in normal clothing (as is the case with most women's examples), it's not an issue. If, however, you have arms full of the things, you are displaying an allegiance to an extreme of fashion closely connected with aggression and anti-social behaviour, and that is not an image that any airline wishes to be associated with.
Obvious, really, innit?!
Scroggs