The premise is backward. After independence (1821), Mexico actively recruited Anglo-Americans to populate Texas as a buffer against Comanche raids and U.S. expansionism.
By 1830, alarmed by Anglo demographic dominance and slavery expansion, Mexico passed the Law of April 6, 1830:
Anglo settlers resisted (Anahuac Disturbances 1832, Convention of 1833). Tensions escalated to revolution (1835) and independence (1836).
Mexico didn't initially object—it invited them. The conflict arose when settlers refused to assimilate and Mexico tried to close the door too late.