Asylum Abuse Reduction Act This bill places restrictions on non-U.S. nationals (aliens under federal law) seeking asylum and contains provisions related to immigration enforcement. Under this bill, an asylum seeker who arrives at a U.S. land port of entry without entry documents may not be admitted unless an asylum officer at a U.S. embassy or consulate has interviewed the individual and has concluded that the individual (1) has been persecuted in the alien's country of nationality due to their race, religion, or other characteristics; (2) has a credible fear of persecution if they returned to that country; or (3) would be tortured by the government upon return to that country. (Currently, an individual arriving at a port of entry may apply for asylum and an immigration officer there typically will conduct a credible fear interview.) Furthermore, an individual who traveled through a third country to enter the United States through the southern border shall be ineligible for asylum unless (1) the individual has applied for and been denied asylum or protection in that third country, (2) the individual was a victim of severe human trafficking, or (3) the third country is not party to certain international agreements relating to refugees. Each federal judicial district shall appoint at least one judge to issue arrest warrants for individuals violating orders to depart, upon a showing of probable cause. Under this bill, the Flores agreement (a lawsuit settlement which imposes various requirements relating to the treatment of minors detained for immigration-related purposes) shall not apply.