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.

Voters will decide on Tuesday whether to keep or repeal the ordinance, which bans discrimination in housing, private employment, city contracting and businesses such as restaurants and bars for 15 protected classes, including race, national origin, age and military status. The City Council approved it last year, but enforcement was put on hold pending the outcome this week.

Proponents said 200 other cities and 17 states had passed similar ordinances to give residents local tools, short of federal lawsuits, to fight discrimination. They worry that a defeat at the polls could generate enough controversy to jeopardize Houston’s status as the host city for the Super Bowl in 2017.