The Mexicans made strong appeals to U.S. troops to switch sides, targeting immigrants and Catholics in particular. Their broadsides emphasized the injustice of the invaders’ cause in the eyes of "civilized people" and stressed what North American Catholics had in common with Mexican Catholics. Alluding to well-known riots by U.S. Protestant nativist mobs, a Mexican pamphlet asked, "Can you fight by the side of those who put fire to your temples in Boston and Philadelphia?" Mexico also offered land grants to opposing soldiers who would desert and claim them: two hundred acres for a private, five hundred for a sergeant. Together, the inducements and propaganda had an effect. The first shots in the war were fired on April 4, 1846, not between Mexican and U.S. troops, but by American sentries at an immigrant deserters swimming across the Rio Grande to the Mexican side…Among three hundred U.S. deserters, the great majority of them Catholics and/or immigrants, joined the Mexican army.
That is from the excellent What Hath God Wrought: The Transformation of America, 1815-1848, by Daniel Walker Howe. The rate of desertion in the Mexican-American War was the highest in American history and twice that of Vietnam.