Trade Preferences and American Manufacturing Competitiveness Act of 2021 This bill reauthorizes and revises specified U.S. trade programs and provisions. Specifically, the bill extends through January 1, 2027, the Generalized System of Preferences (GSP), which provides duty-free treatment to products imported from designated beneficiary countries. The bill makes various changes to the GSP, including by (1) adding human rights, environmental, and other criteria for designation as a beneficiary developing country; (2) requiring an assessment of how the GSP supports worker and gender rights; and (3) requiring a study on rules of origin and GSP utilization rates. Additionally, the bill provides through December 31, 2023, and retroactively applies to 120 days before this bill's enactment, temporary duty suspensions or reductions to eligible imported products. This authorization is commonly known as the Miscellaneous Tariff Bill (MTB). The last version of the MTB was enacted in September 2018 and the temporary treatment for those products listed in the MTB expired on December 31, 2020. The bill also extends the American Manufacturing Competitiveness Act of 2016 for two future MTB cycles (one in 2022 and one in 2025). This extension allows the U.S. International Trade Commission to conduct the MTB petition, review, and recommendation process for those additional cycles. The bill extends customs user fees through June 21, 2031.