In my field (childcare) they don't really care what tats/piercings you have. But I know my friend works in a dental office and they don't want her to have any tats and she has to take out all of her piercings before she goes in. It just depends.

But wrists tats, as people have said, are easy to cover and actually often go unnoticed. I know people who didn't realize I had mine until a good year after wards.