Civil Rights Modernization Act of 2021 This bill specifies that the federal liability protection that a provider of an interactive computer service (e.g., a social media company) receives for content provided by third parties does not apply to certain advertisements that target users who are part of a protected class or have a protected status. Specifically, the liability protection shall not apply to investigations, claims, or charges arising under civil rights laws if the provider (1) receives consideration (e.g., money) for publishing or delivering an advertisement; and (2) uses an algorithm, software application, or other information technology to target the advertisement to a user who is part of a protected class or has a protected status.