The best explanation for why the Mexican government allowed Anglo-American settlers to bring enslaved people to Texas is:
The Mexican government wanted Anglo-Americans to buy land in Texas.
The Mexican government encouraged settlement in Texas to help develop the area, and they saw the influx of Anglo-American settlers, who often brought enslaved people, as a means to achieve that goal. However, it is also important to note that by the time of the Texas Revolution in the 1830s, sentiments regarding slavery were shifting within Mexico, but initially, the focus was on attracting settlers.