The answer is both yes and no. There is no law in Texas that allows equal access in public accommodations to anyone for any reason. Federal and state laws cover all protected classes contained in this ordinance in fair housing except sexual orientation and gender identity. Federal law provides equal access in public accommodations and employment protections for all of those same classes, but again excludes sexual orientation and gender identity. Texas employment protections also exclude sexual orientation or gender identity.
The difficulty for people who face discrimination is that there is no local mechanism for making complaints of discrimination. Complaints must be filed with federal or state agencies using a complicated and lengthy process. In some cases, the only option is to file a lawsuit in federal district court, which is extremely expensive and takes a very long time. This ordinance allows the City of Houston Office of Inspector General (OIG) to review and investigate complaints to deal with them quickly and easily - usually without the need to hire an attorney. The OIG can still refer complaints to federal or state agencies if it becomes necessary.