Biodiesel, Renewable Diesel, and Alternative Fuels Extension Act of 2021 This bill extends and modifies the tax credits for biodiesel, renewable diesel, and alternative fuels. The bill extends through 2025 (1) the income tax credit for biodiesel and renewable diesel used as fuel, (2) the excise tax credit for biodiesel mixtures, (3) the excise tax credit for alternative fuels, (4) the excise tax credit for alternative fuel mixtures, and (5) the payments that are equivalent to the excise tax credits for biodiesel mixtures and alternative fuels. Beginning in 2023, the bill phases down the credits for biodiesel, biodiesel mixtures, alternative fuels, and alternative fuel mixtures by reducing the credits by specified amounts.