Yes, you can wear jewelry in Belize and feel safe. The only place where you won't be safe is if you go on the south side of Belize City wearing your bracelets, expensive rings, and necklaces. You might as well paint a target sign on your back or put a sticker on you that says "Rob me!"
Going to San Pedro on Ambergris Caye and the areas where there are lots of tourists and expats, yes, you can wear your jewelry. We recommend wearing jewelry during the day and in well-lit areas. In crowded areas it's safer. Don't go into dark alleys either wearing your jewelry or being alone. It is relatively safe during the day having jewelry on while staying in the safe zones, I would say.
I personally don't have any problem wearing my jewelry. I wear jewelry, for example, on weekends, and going to the grocery store. It is no problem during the day. I wouldn't wear any heavy jewelry and go into south side of Belize City.