Balancing the Rights Of Web Surfers Equally and Responsibly Act of 2021 or the BROWSER Act of 2021 This bill establishes information privacy protections that require broadband internet access services and certain websites or mobile applications to provide users with the ability to opt-in or opt-out of the using, disclosing, or accessing of their user information depending on the sensitivity of the information. Covered service providers must provide opt-in approval through express user consent to use sensitive information such as financial data, health information, browsing history, or other specified personally identifiable information. Such service providers must obtain opt-out approval for the use of non-sensitive user information by a user failing to object to such use after being provided notice of the provider's privacy policies. Service providers also must allow users to opt-in or opt-out of such approval at any time. The bill permits service providers to use and disclose user information without approval for specified purposes, including for services necessary for provision of the service and to initiate, render, bill, and collect for the service. The bill further prohibits providers from conditioning access to service on users' agreeing to waive their privacy rights.