Personally I'd view this quite positively, assuming the tattoo looks good. It shows a bit of something about her character. I feel the same way about girls who dye their hair certain colours, for example I prefer bottle blondes to natural blondes.
And if it wasn't my particular style, it wouldn't be relevant really. I doubt it's going to put anyone off.
If you want to know the answer, just reverse it - you meet a guy you really like who has the same thing. You gonna dump him for it?