Synthetic fertilizers very rarely, but pesticides are used (insecticides and fungicides). Also, straw can come from conventional farms and might have pesticide residues in it. And where cottonseed meal is used, that might be a
GMO.
In some places to sell something as Organic, you need to have your property certified by the industry. So even if you don't use synthetic fertilizers or pesticides on your mushrooms, you still can't sell them as Organic.