Will this ordinance really allow men into the womens restroom?

Answer

No.  This is is a false claim that has been used by opponents of equal rights laws across the country for years.  The City of Houston already has a law* that makes it illegal for a person to enter a restroom of the opposite sex to cause a disturbance.  That law has been in effect for almost 50 years and will continue to remain in effect.

*Code of Ordinances, Sec. 28-20. Entering restrooms of opposite sex.