A healthy tan is one thing, but orange is quite another. I am an alumna of another Florida school, and we were also requested to have tans for recruitment. I never got a tan! I am very pale, so pale my dermatologist calls me "her pale person".
I cannot get a tan because of some scares with Melanoma. I just addressed this to my VP of membership and it was never a problem.
As a PNM, I would try to get your skin to look as healthy as possible and be yourself. It is unrealistic to think that every PNM is going to have tanned skin. Everyone's skin tone is different and some people have a naturally pale or darker skin.