So I was a little confused by this, so I thought I'd look into it a bit.
Apparently Texas doesn't have a state-wide non-discrimination law. So you can be discriminated against for being male, female, transgender or you can be discriminated against for being gay, straight, bisexual, whatever. The only law that would protect you from discrimination would be any existing federal laws.
But all some people seem to focus on is the bathroom thing. Apparently the section prohibiting locker room discrimination was removed well before the ordinance was brought up for a vote.... So the people who voted against it were NOT voting against some transgenders using bathrooms ordinance... they were voting against a standard equal rights ordinance.
Keeping it Klassy houston.