Although cottage food operations cannot sell items that require refrigeration, I believe that almost any gluten item that would be allowed under the law would also be allowed if produced gluten-free. Gluten-free items may not have as long of a shelf life and refrigerating them may help preserve them, but they probably wouldn’t become potentially hazardous if left unrefrigerated. If they simply become moldy, then they aren’t hazardous, despite being undesirable. Cottage food products can be refrigerated, but they just cannot require refrigeration, like meats do. A lot of CFOs across the country do sell gluten-free baked goods.
You cannot ship to other states.
I hope that helps, and let me know if you have more questions.