The straight answer to this is yes. You can recycle rubber bands. But, this answer only seems straightforward. The process is much more complicated than it sounds.
Sustainability performance of polyethylene terephthalate, clarifying challenges and opportunities - Sarda - 2022 - Journal of Polymer Science - Wiley Online Library
Are Rubber Bands Recyclable? (And Ways To Recycle Old Bands) - Conserve Energy Future
New Start-Up Aims to Recycle Those Gross Rubber Bands You Had to Wear with Braces – Eritas Daily
Crocs — Design Life-Cycle
How to Recycle Keys or Put Them to Good Use
Comprehensive Recycling and Disposal Guide
Polymers, Free Full-Text
Monster High Dolls — Design Life-Cycle
Recycling, Free Full-Text
Alliance Rubber 02005 EPDM Non-Latex Rubber X-treme File Bands, 200 Units (7 x 1/8, Lime Green), 175 packs : Large Rubber Bands : Office Products
Kids Super Guide to Recycling