Veterans Visa and Protection Act of 2017 This bill requires the Department of Homeland Security (DHS) to: (1) establish a program to permit an eligible deported noncitizen veteran to enter the United States as a lawful permanent resident alien and permit an eligible noncitizen veteran in the United States to adjust to lawful permanent resident status, and (2) cancel an eligible noncitizen veteran's removal and allow the individual to adjust to lawful permanent resident status. A veteran is eligible if the veteran has not been convicted of a crime of violence or a crime that endangers national security for which the veteran has served at least five years in prison. DHS may waive eligibility requirements for humanitarian, family unity, public interest, or exceptional military service reasons. A noncitizen veteran or service member may not be removed from the United States unless such individual has been convicted of a crime of violence. An individual who has obtained lawful permanent resident status pursuant to this bill shall be eligible for: (1) military and veterans benefits, and (2) naturalization through U.S. military service.