The GOP will never win over a group that cannot assimilate into the USA. Hispanics, like blacks, are not coming to the (alleged) party of smaller government.
Better to invest in Asian outreach.
There are several millions of Hispanics in Texas whose families have been here since Independence -- and before -- who would sharply disagree with your conclusion.
There were many Hispanics inside the Alamo...and at Washington-on-the-Brazos.
Your description may be accurate for the late arriving illegals, but it's not accurate for the bulk of legal Hispanics.