While laws regarding this topic within Texas are not yet in place, the law will likely match the US laws on the topic. Those being that a US citizen cannot lose their citizenship simply for living in another country.
Spouses make matters a little more tricky. While there is no question that a Texan citizen and their spouse may reenter the independent Texan nation to live, the spouse may have to apply for a ‘green card’ and complete a number of years in the country before becoming a full citizen, like in the US. However, there are no concrete laws on this matter, and after independence, it will be up for debate among the Texas State Legislators.