Final answer:
Free African Americans were prohibited from settling in Texas, as tensions between American settlers and the Mexican government escalated due to cultural, religious, and slavery issues.
Step-by-step explanation:
The group that was prohibited from settling in Texas was free African Americans. The Mexican government initially welcomed American settlers into the Texas territory with the expectation that they would integrate into Mexican society by adhering to their laws, which included official transactions in Spanish, settling into the interior of Texas away from the U.S. boundary, and becoming Roman Catholic.
However, tensions escalated due to cultural, political, and economic differences, most notably the Americans' desire to practice Protestant religion and own slaves. The Mexican government had passed laws to limit the institution of slavery, which were largely ignored by American slaveholders. Subsequently, the prohibition of the future U.S. immigration came into effect in 1830 due to the reluctance of these Americans to comply with Mexican laws and their growing numbers, which posed a threat to Mexican sovereignty over Texas.