A group of conservative Christians set out to block El Paso, Texas, from granting health-care benefits to same-sex partners of city-government employees. But the ballot measure they helped pass in November may also end up stripping benefits from others, including retired policemen and firefighters.

The measure was aimed at gay workers and their partners. The wording of the proposal, however, was vague, asking El Paso residents to endorse "traditional family values" by limiting benefits to "city employees and their legal spouse...