Veterans State Eligibility Standardization Act This bill requires the Department of Veterans Affairs (VA) to make modifications related to areas of residence and variable income thresholds for purposes of determining whether veterans qualify for treatment as low-income families for enrollment in the VA health care system. The bill also requires the VA to ensure that all veterans who enroll in the VA health care system remain eligible to continue receiving health care furnished by the VA, subject to cost-sharing requirements that apply under current law.