National Origin-Based Antidiscrimination for Nonimmigrants Act or the NO BAN Act This bill imposes limitations on the President's authority to suspend or restrict aliens from entering the United States. It also prohibits religious discrimination in various immigration-related decisions, such as whether to issue an immigrant or nonimmigrant visa, unless there is a statutory basis for such discrimination. The President may temporarily restrict the entry of any aliens or class of aliens after the Department of State determines that the restriction would address specific and credible facts that threaten U.S. interests such as security or public safety. The bill also imposes limitations on such restrictions, such as requiring the President, State Department, and the Department of Homeland Security (DHS) to (1) only issue a restriction when required to address a compelling government interest, and (2) narrowly tailor the suspension to use the least restrictive means to achieve such an interest. Before imposing a restriction, the State Department and DHS shall consult with Congress. The State Department and DHS shall report to Congress about the restriction within 48 hours of the restriction's imposition. If such a report is not made, the restriction shall immediately terminate. Individuals or entities present in the United States and unlawfully harmed by such a restriction may sue in federal court. DHS may suspend the entry of aliens traveling to the United States on a commercial airline that failed to comply with regulations related to detecting fraudulent travel documents.