Department of Veterans Affairs Contracting Preference Consistency Act of 2020 This bill requires the Department of Veterans Affairs (VA) to give preference to nonprofit firms that employ the blind and significantly disabled when contracting for covered products and services that are included on the procurement list maintained by the U.S. AbilityOne Commission. The commission provides employment opportunities for people who are blind or have significant disabilities. The bill provides an exemption in certain situations for covered products or services for which contracts were awarded after December 22, 2006, and were in effect on the day before the enactment date of this bill. A covered product or service is one that was included on the commission's procurement list on or before December 22, 2006, or a product or service that (1) is a replacement for a product or service on the commission's procurement list, (2) is essentially the same and meets the same requirements as the product or service being replaced, and (3) meets the VA's quality standards and delivery schedule.