I think this is the wrong argument.
Switch on the TV today and watch for a few hours.
Count how many people are on the box who are not white. Then look at their skin tone.
Whether it is a newsreader, actor, TV presenter, you will find pale skin. The only time you see very dark skin in sports, or where a sports person has moved from playing/competing to commentating.
Britain is a majority white country with significant numbers of people from all corners of the earth with all skin tines, but you wouldn't know that from watching TV.
It should absolutely be up to someone what they do to their skin, whether they have tattoos, piercings, bright pink hair etc.
It is also right that in some jobs certain ways of dressing are accepted as the norm and tattoos need to be covered / piercings removed.
But the big difference is that doing something to your body may make you less employable, changing your skin tone should not make you more employable.
Can you imagine if getting a job depended on you having a tattoo or a piercing? That in order to get a job you have to permanently do something to your skin that may well damage it?