Responsibly Addressing the Marijuana Policy Gap Act of 2019 This bill removes federal restrictions on, and creates new protections for, marijuana-related conduct and activities that are authorized by state or tribal law (i.e., state-authorized). Among other things, the bill does the following: eliminates regulatory controls and administrative, civil, and criminal penalties under the Controlled Substances Act for state-authorized marijuana-related activities; allows businesses that sell marijuana in compliance with state or tribal law to claim certain federal tax credits and deductions; eliminates restrictions on print and broadcast advertising of state-authorized marijuana-related activities; creates protections for depository institutions that provide financial services to marijuana-related businesses; specifies that a marijuana-related business is entitled to federal bankruptcy protections; establishes a process to expunge criminal records related to certain marijuana-related convictions; reestablishes federal student aid eligibility for certain students convicted of a misdemeanor offense for marijuana possession; exempts real property from civil forfeiture due to state-authorized marijuana-related conduct; prohibits the inadmissibility or deportability of aliens for state-authorized marijuana-related conduct; specifies that drug-related criminal activity, which is prohibited in federally assisted housing, does not include state-authorized marijuana-related conduct; establishes a new, separate registration process to facilitate medical marijuana research; authorizes health care providers employed by the Department of Veterans Affairs to recommend participation in state marijuana programs; and authorizes medical providers through an Indian health program to make medical recommendations regarding marijuana.