Hey, I've been skimming through red foot posts as a newer red foot owner myself trying to learn as much as I can and saw no one has answered your post yet. I am no expert on redfoot diet but I am much more knowledgeable about mushrooms. I teach a wild edibles class that includes mushrooms. The only mushroom that I have ever seen recommend to feed a redfoot is the button mushroom (classic grocery store white mushroom) these however are a cultivated species and are not found in the wild, its closest relative is the field mushroom which looks very much like the button mushroom. However, if you are not familiar with mushroom ID I would not recommend you or your tortoise eating any mushrooms you find out In the wild. There are several mushrooms (particularly in the Amanita family) that can be deadly after just a few bites to a full grown person let alone a tort. If your interested in wild plants to feed your shelled friend, my two little hatchlings love dandelion, wintercress, wood sorrel, red clover, sheep sorrel and lambs quarters. Hope this helped!
I would say that any mushroom that is safe for humans to eat, are fine for torts as well. Mine go crasy for champignons (white with brown underside) as well as chanterelles. Mushrooms here in Sweden are very seasonal, so store bought champignons unless I can pick chanterelles.