Maybe because Hispanics are generally devout Catholics who do like the idea of getting the church more involved in people’s lives and don’t like the idea of abortion very much.
And those who got here legally, became citizens and have the right to vote generally do not care much for illegals; the attitude is, “I had to wait my turn; so can you.” And those who are second-gen or third-gen or twelfth-gen are even more likely to be hostile towards illegal immigrants, not less.
Also, Hispanics are not exactly a marginalized race in Texas. In fact, many Texans don’t even consider Hispanics a different race from whites; both “races” are a mixture of European and Native American descent. The only real difference is that white Texans tend to be Protestant, and Hispanic Texans tend to be Catholic.
Really, we can come up for reasons why the hispanic electorate is shifting to the GOP all day. You can say it’s because they’re a bunch of dumbasses who don’t realize how those Evil Republicans are out to kill them all; I can say it’s because the GOP happens to have policies that appeal to the demographic. It’s shifting either way.