Citizen Justice Restoration Act of 2020 This bill prohibits decisions to search, seize, or scrutinize an individual that discriminate on the basis of race, ethnicity, national origin, religion, or sex. Specifically, the bill prohibits a person acting under color of law from basing a decision to search, seize, or scrutinize an individual on actual or perceived race, ethnicity, national origin, religion, or sex, including sexual orientation, and makes evidence obtained as a result of such a search or seizure inadmissible, with exceptions; requires an application for a writ of habeas corpus on behalf of a person in custody pursuant to the judgment of a state court to be granted with respect to any federal claim that was adjudicated on the merits in state court proceedings, which adjudication was in error; makes a new rule of constitutional law announced by the U.S. Supreme Court, a U.S. Court of Appeals, or a U.S. District Court retroactive to cases on collateral review; and requires an ambiguity in a statute that provides protection against discrimination on the basis of race, color, ethnicity, national origin, religion, disability, or sex to be construed in the manner that will provide the greatest protection against such discrimination. The bill further creates a private right of action and provides for the award of a bounty for citizen lawsuits under specified circumstances.