United Nations Voting Accountability Act of 2021 This bill prohibits giving assistance, such as various types of economic support or military training, to countries that opposed U.S. positions on more than 50% of the recorded votes in the most recent United Nations session. A country may be exempted if there has been a fundamental change in the country's leadership and policies and the Department of State determines that the country will no longer oppose the U.S. position. The President may also exempt a country for U.S. national security interests.