Most conservative “hispanics” probably self-identify as white and have been here for generations.
Just among conservatives I know I can think of 6 or so who are hispanic, in the US and not native born - none fit your template. Some are citizens, others are on their way, others were just here temporarily. I can think of many other people I’ve known or met briefly who are living in central or south America who are conservative. I’ve also met a few hispanics from many places who are liberal, some radically so.
Anecdotes aside, suppose you are correct in your assessment. Should their votes be sought with different speeches? Should we appeal to conservative US citizens of hispanic origin with a different ‘conservative message’ than we use for other conservative US citizens who have different ancestries or nations of birth? If so, how would those messages differ? Should we hyphenate conservative ideas?