Is it ok to wear jewelry to dance class?

The common, general answer to this question is "no," but there are always exceptions and deeper explanations.  My answer is "it varies based on the style of dance and style of jewelry in question." (Note: Always obey dress codes and studio rules, even if they contradict what I say.)

There are three big reasons not to wear jewelry to dance.  1) It can be dangerous.  2)  It can look unprofessional.  3) It can impair technique.  Not all pieces of jewelry are dangerous, unprofessional, or impair technique, and some are harmful in some styles of dance and innocuous in others. 

If you do a style of dance that involves turns, jumps, fast movements, and/or moving close to other people, then all necklaces, all bracelets, large/hoop earrings, and large rings can be dangerous. They can fly off while you are moving and hit someone.  If you do partnering, pretty much any rings can be dangerous or impair technique.  It's more difficult to grab hands when rings could get in the way.  Rings with stones can scratch your partner during quick hand grabs.  For all styles of dance, large, heavy, or "swinging" jewelry can throw off your technique. 

For technique classes in ballet, jazz, tap, and modern, it's ok to wear small post earrings, small well-fitting rings, and secure watch-like wristwear like fitbits or heart monitors.  Leave all other jewelry at home.  For any partnering class or ballroom/Latin class, take off rings and wristwear.  Only wear small post earrings, and put post jewelry in any body piercings.

At auditions, summer intensives, or placement classes, it's important to look serious and professional.  Never wear ankle bracelets.  They look bad both under and over dance tights.  Show that you respect the rules and the safety of others by taking off all jewelry except small post earrings and subdued post body jewelry (small well-fitting rings are ok if there is no partnering).