Texas and other states can require proof of citizenship for voting and getting drivers' licenses. The SCOTUS decision only related to voter registration. Currently in Texas, you can register a voter even though they do not have the required photo id. Under federal law, a first time voter who did not provide a social security number or drivers' license can be required to show id before voting for the first time.
The SCOTUS decision that you mentioned was related to the State of Arizona's attempt to add a citizenship proof in order to registered. Arizona's requirement would be in addition to and conflict with the federally approved form of voter registration that is authorized by Federal law.
In Texas, you have to provide proof of citizenship to get a new drivers' license. You do not have to provide proof of citizenship to get a concealed carry permit in Texas and that is also one of the approved forms of photo id allowed under the Texas voter suppression law. http://www.juanitajean.com/2011/09/18/texas-handgun-permit/
....Only one of those five items does not require you to produce proof of citizenship.
Its the license to carry. You do not have to prove citizenship to get a license to carry a gun in Texas. On September 10, 2001 Mohamed Atta could have gotten a license to carry in Texas.