Anti Digital Redlining Act of 2021 This bill prohibits an internet service provider (ISP) from discriminating in decisions about deploying or upgrading broadband service in a particular geographic area based on residents' race, income, or other factors (i.e., digital redlining). It also prevents some restrictions on the choice of telecommunications service providers in multi-dwelling units. The Federal Communications Commission (FCC) must solicit public comments on criteria to determine whether an ISP is discriminating in deployment or upgrading decisions and related matters. Based on the comments, the FCC must issue rules to prevent such discrimination. An individual may file a complaint of discriminatory conduct that violates the bill's provisions or applicable rules with the FCC. The bill authorizes the FCC to remedy violations, including by requiring (subject to limitations) an ISP to provide services in a geographic area. Additionally, the bill prohibits ISPs and multichannel video programming distributors (e.g., cable operators) from engaging in certain conduct that restricts a multi-dwelling unit resident's choice of internet, cable, and related services. Units must also allow ISPs and distributors reasonable access to their premises. The bill permits residents to sue for violations and otherwise provides for enforcement through FCC administrative processes. The FCC must also analyze the use of franchise agreements between telecommunications service providers and municipal governments on the price of, quality of, and competition among telecommunications services in the local market. These agreements set out the terms under which a telecommunications service provider is authorized by a regulator to operate.