Actually, the flag height business is untrue.
Wikipedia’s version
“It is a common urban legend that the Texas flag is the only state flag that is allowed to fly at the same height as the U.S. flag. Allegedly, Texas has this right inherently (as a former independent nation) or because it negotiated special provisions when it joined the Union (this version has been stated as fact on a PBS website[10]). However, the legend is false. Neither the Joint Resolution for Annexing Texas to the United States nor the Ordinance of Annexation[11] contain any provisions regarding flags. According to the United States Flag Code, any state flag can be flown at the same height as the U.S. flag; the U.S. flag should be on its right (the viewer’s left), however. Consistent with the U.S. Flag Code, the Texas Flag Code specifies that the state flag should either be flown below the U.S. flag if on the same pole or at the same height as the U.S. flag if on separate poles.[3]”
And the Snopes version.
In addition, all 50 US states function as republics, and all 50 states are voluntary members of the federal republic that is the United States. Texas is not special in that regard. It is not both a state and a republic in any way different than any other state. However, Texas did not have to change its flag, its seal, or the way it ran its business, except to replace the word republic with the word state. The folks running things in the republic all transferred over to run the same things in the state.
Nonetheless, I am proud to be a Texan and consider it to be a special place.