Hispanic voters are Legal (heck they're citizens) and they vote Democratic.
It's not illegals who make those Texas border counties democrat strongholds.
What proportion of illegals vote, do you suppose?
With "Motor Voter" and many states granting driver's licenses to illegals plus, in some states, same day registration, just how many millions of illegals vote?
And, while I'll agree with your observation on the Texas border counties, legal Hispanics in those counties are more likely to vote Republican than the illegals -- who will vote Democrat virtually unanimously.
Indeed, Corpus Christi now has a Republican Congressman. And some of the other South Texas districts are increasingly competitive. Further, legal Hispanics in Central and North Texas are even more likely to vote Republican.
Finally, it's not really a question of gaining majority support from Hispanic voters for Republicans. Currently, the GOP gets about 30% of the Hispanic vote nationally (which includes a few millions of illegal Hispanics). If we could build that number to just 40%, the Democrats would be hard-pressed to win another national election.
I would submit that 40% is eminently doable -- especially if we can get voter fraud under control.