Final answer:
The requirement not necessary for joining Stephen F. Austin's group of settlers was 'They had to give up their rights as U.S. citizens.' The settlers were required to become Catholic and pledge loyalty to Mexico, but formal renunciation of U.S. citizenship wasn't mandated. The correct option is D.
Step-by-step explanation:
The requirement for joining Stephen F. Austin's group of settlers that was not a condition is D. They had to give up their rights as U.S. citizens. The settlers who came to Texas under the invitation of the Mexican government were expected to integrate into the local population and society. According to the colonization laws set by Mexico, American settlers were required to pledge loyalty to Mexico, which did imply a recognition of Mexican authority over Texas.
However, they were not required to formally renounce their U.S. citizenship as a condition for settlement. They were expected to adopt the Catholic religion as Mexico, after gaining independence from Spain, wanted to promote Roman Catholicism. Despite this expectation, many American settlers retained their Protestant beliefs, and the Mexican government's hopes of integrating the Americans culturally and religiously were largely unsuccessful.
The settlers were indeed different from the local population, referred to as tejanos, in several respects including religion and the practice of slavery, which was contentious within Mexican law.