Allowing Greater Access to Safe and Effective Contraception Act This bill requires the Food and Drug Administration (FDA) to prioritize review of supplemental drug applications (applications to modify the approved use of a drug) for contraceptive drugs intended for routine use that would be available to individuals aged 18 and older without a prescription. The FDA must waive user fees for such supplemental drug applications. Any drug that is eligible for this priority review must be a prescription drug for individuals under age 18. This bill repeals provisions of the Patient Protection and Affordable Care Act and the Health Care and Education Reconciliation Act of 2010 to allow health savings accounts and health flexible spending accounts (HFSAs) to be used to pay for medicine without a prescription and to remove the limit on salary reduction contributions to a HFSA under a cafeteria plan, effective as if the provisions had never been enacted.