Local News and Broadcast Media Preservation Act of 2020 This bill modifies ownership rules and limitations related to media such as newspapers and broadcast stations. Specifically, the bill repeals specified media ownership limitations and prohibits the Federal Communications Commission from disallowing multiple ownership of radio and television stations. It also prohibits the Federal Trade Commission from considering whether certain media mergers will substantially lessen competition or tend to create a monopoly. Further, the bill creates a four-year safe harbor from antitrust laws for print or digital news companies to collectively negotiate with online content distributors (e.g., social media companies) regarding the terms on which the news companies' content may be distributed by online content distributors.