Gay and transgender individuals face a sweeping rollback of health-care protections under a Trump administration proposal that goes further than anticipated.

The proposal, released May 24, is intended to strip away an Obama-era rule prohibiting discrimination against transgender people and women seeking abortions. But it would also strike sexual orientation protections from regulations for programs like Medicare and Medicaid, going further than what health-care policy researchers were expecting and weakening protections for the overall LGBT community.

The Trump administration...