Of course it'a possible. It's easily proven by seeing how many shy people are nudists. Among nudists, there are different levels. I doubt a shy person will be a top level exhibitionist but they can enjoy nudity with others.
It comes down to how you feel about yourself and view yourself. Been shy can be a good thing as you are more true to others when you finally get the never to step forward. In the cloth world, individuals that are shy are made to feel less for it while others feel they don't fit in with others for various reasons.
In the true nudism world, individuals dont care, as most have wrote, it's a freeing of oneself. As I saw one sign once, nudist see their friends as they are. There is nothing to hide behind, you are in your natural skin and take pride in that.
I'm a shy person - bit of an introvert - but when I made my first visit to our nude beach, it felt perfectly normal to get naked. I wasn't embarrassed or worried about what other guys thought. Quite freeing.
I was very shy and still am around many new people, nudism helped me let bled.
J
I'm a very shy person. When I go to events alone, it's very hard for me to go up to people and talk with them. I much prefer to sit alone and not bother anyone. I've always been a very quiet, private person. Being a nudist hasn't really changed that for me at all. When I have gone to the nude beach alone, I sit alone and really don't talk to anyone else. If someone approaches me to talk, I'll talk to them, I'm not rude, it's just not easy for me to make the first move. I'm the same way nude or wearing clothes.
If you view nudity as just a form of exhibitionism or even as exposing yourself, then I guess it would be hard for a shy person to become one. But if you simply accept that to be naked is a perfectly natural state to be, it's very easy to strip off and just be yourself, be that quietly and reservedly or in a more outgoing and sociable manner.