Conservation Reserve Program Flexibility Act of 2021 or CRP Flexibility Act of 2021 This bill modifies the Conservation Reserve Program (CRP) to permit emergency haying during the primary nesting season to respond to drought or other emergencies. (Under current law, emergency haying is only permitted outside of the primary nesting season.) Under CRP, the Department of Agriculture provides annual payments to agricultural producers to take highly erodible and environmentally sensitive land out of production and install resource-conserving practices.