I think nuns being in a beauty contest is fine, so long as they don't make a habit of it...
Smart ass.
Anyway, this sort of surprises me. When a nun becomes a nun, they take three vows - of poverty, chastity and obedience. I can't imagine which superior would allow nuns from their order to participate in this - one of the big things for nuns is their humility, which is part of why they wear veils - to humble themselves. It's not too humble to post pictures of yourself on the Internet with the express desire to have them seen by many people. Most nuns I know of would
never want that to happen. One nun in particular that I know well recently retired from teaching at my old Catholic school after fifty-eight odd years of teaching, and we honored her immensely - we got her a regional teacher award that was put on TV, she got the diocesan award for teachers, and we dedicated our spring musical to her. She hated every moment of it because she didn't like being put in the spotlight at all.
Besides, the recent trend in orders of sisters is the more traditional orders who would never allow this. A lot of the girls are going for the full habits, not the modern orders.