Veterans' Preference Parity Act This bill modifies the eligibility criteria for certain veterans to qualify for a preference in the federal hiring process. Specifically, an individual who is honorably discharged from active duty service is eligible for a veterans' preference, if the active duty service was performed for more than 180 total days (currently, consecutive days). Additionally, a retired member of the Armed Forces is eligible for a veterans' preference, even if the retiree (1) is not a disabled veteran and (2) retired at or above the rank of major or its equivalent.