According to the Farm Service Agency and Farm Credit, it's difficult to lend to non-profit farms because there is no way to prove that you will have the future cash flow necessary to pay back the debt.
Most Farm Credit and FSA representatives have not even considered lending to a non-profit institution before so We do not recommend that non-profit farms apply for a loan.
You can call your local FSA or Farm Credit institution to confirm this in your area.
It's possible that there may be some microloans available to non-profit farms through the USDA. Call your local service center to learn more: https://offices.sc.egov.usda.gov/locator/app