Circumspectly Reducing Unintended Consequences Impairing Alliances and Leadership Act of 2021 or the CRUCIAL Act of 2021 This bill establishes requirements relating to the President's ability to impose sanctions on individuals or entities that engage in a significant transaction with the defense or intelligence sectors of Russia's government if the transaction involves a member of the Quadrilateral Security Dialogue. (The dialogue is a coalition comprised of the governments of the United States, Japan, India, and Australia.) Specifically, before imposing such sanctions for a transaction involving a member of the dialogue, the President must certify to Congress that the government in question is not participating in the dialogue on security matters that are critical to U.S. strategic interests.