School Food Modernization Act of 2021 This bill provides for loan guarantees and grants to support healthy meals under the National School Lunch Program and School Breakfast Program. The bill directs the Department of Agriculture (USDA) to issue loan guarantees to local educational agencies (LEAs), school food authorities, tribal organizations, and other eligible entities to finance infrastructure improvements or equipment purchases to facilitate their provision of healthy meals through the school meal programs. USDA must also award competitive matching grants to assist LEAs, school food authorities, tribal organizations, and other eligible entities in purchasing the durable equipment and infrastructure they need to serve healthier meals and improve food safety. USDA must give preference under both programs to applicants that demonstrate a substantial or disproportionate need for food service infrastructure or durable equipment, and shall establish fees for the loan guarantee program. In addition, USDA must award competitive matching grants to experienced third-party training institutions to provide school food service personnel with the training and technical assistance they need to (1) meet or exceed nutrition standards under the school meal programs, and (2) improve the efficacy and efficiency of the school meal programs.