When I first started rebounding, everyone (on the internet) said to rebound barefoot. No one asked if I had any previous injuries or health conditions. There were no form or alignment instructions either. Sure enough, 6 months into consistently rebounding and my knees started aching. I scoured the internet and found some videos discussing form. I made adjustments and things got better, but I still had a nagging ache from a knee injury I sustained a few years prior. I decided to go to a running store and get fitted with high quality trainers. I started wearing them while rebounding. My knees are SO MUCH better! Shoes provide the extra support I need and I've decided that is absolutely OK!
If you are healthy, active, using good form and want to rebound barefoot, by all means you should do it! Barefoot is a great way to build proprioception in your feet which helps improve balance. I'm all for rebounding barefoot if it works in your body.
You are the expert and authority of your body. At the end of the day, you should do what feels best for you, especially if you have any previous injuries. Personally speaking, I like shoes. I wear Saucony, but there are lots of good brands available. You'll still see me barefoot from time to time, but only when I consider it a gentle workout. I wear shoes for anything moderate to high intensity.
My advice...try both! See which you like best. It doesn't have to be any more complicated than that.
Nikki (Earth & Owl)