There is a great difference between tasteful piercings and tattoos just as there is a difference between someone who looks like a clown in their multi-colored scrubs or trashy in their too small pants with underwear showing. Makeup is another big one for looking unprofessional. I see tattoos and facial piercings as no different--if piercings are tasteful and conservative in jewelry choice or well done in the case of tattoos, if your makeup is tasteful, your uniform is sharp and your hair is tidy and pulled away from your face, you have a smile on your face and treat your patients with respect they shouldn't matter.
1) As for facial jewelry, don't wear something unsafe. No down to the shoulder hoops or multiple big pieces of jewelry or otherwise.
2) Tattoos are here to stay. Literally. Make sure they are not offensive and if they are poorly done, go get them fixed. To gain legitimacy, tattoos should be artwork, not crap.
3) Keep it clean. For the person who was concerned about infection control related to piercings? I would be more concerned about the continued lack of hand washing in the healthcare world.
For the record, I am a nurse practitioner who is fully sleeved, have my ears gauged (that means my lobes are stretched to a zero gauge---same as IV sizes) and have a very small nose stud. In my experience my patients of all ages ask about my art work and it creates an almost immediate personal conversation piece to break the ice. I ensure that when at work, my ears have tasteful jewelry, I do NOT wear rings on my hands for infection control reasons.
I have never been accused of being disrespectful because it isn't my appearance that determines how I treat my patients---my actions and caring attitude to that.