HOUSTON — Outside a polling station near this city’s wealthy River Oaks neighborhood, dozens of campaign signs plastered with the names of candidates line a busy section of West Gray Street. But a few stand out for their lack of names and their stark message in black and red letters: “No Men in Women’s Bathrooms.”

These are strange, divisive times in Houston.

An election battle over the city’s equal rights ordinance has turned into an expensive and bitterly fought culture war, pitting some of Houston’s most powerful pastors and social conservatives against its mayor, who is a lesbian, and her supporters. Opponents have zeroed in on the protections it would give for gender identity, particularly transgender Houstonians who were born male but identify as women.