Asylum Reform and Border Protection Act of 2021 This bill makes various immigration-related changes, such as restricting Department of Homeland Security (DHS) authority to parole certain aliens. The bill (1) bars the government from paying for counsel for a person in any immigration proceeding before DHS or the Department of Justice, whereas currently the prohibition only applies to removal proceedings; and (2) raises the burden on an alien to establish the alien's claimed fear of persecution when seeking asylum. DHS shall standardize questions asked in expedited removal proceedings and record such proceedings. DHS may parole an alien into the United States only on an individualized basis and may not use eligibility criteria describing an entire class of people. The bill imposes additional restrictions on such parole authority. The bill removes an exception which allows an unaccompanied alien child to seek asylum while in the United States (or upon arrival at the U.S. border) even if the child may be removed to a safe third country where the child may seek asylum. The bill also bars an alien from seeking asylum while in the United States (or upon arrival at the U.S. border) if the alien may be removed to a safe third country where the alien may seek asylum. Currently, this bar only applies if the United States has an agreement with the third country. The bill bars several grounds for asylum related to generalized violence. The bill expands what constitutes a frivolous asylum application to include those filed solely to delay removal, among others. Currently, an application is frivolous only if any material elements are deliberately fabricated.