Here’s the thing, most hispanics in this country are of Mexican birth/background. Rubio is Cuban and I think that would prevent him being seen as “one of us” by most Hispanics.
That’s something I have noticed since moving down here, there is very much an ethnic pride.
Same goes for the Haitian/Jamaican/Virgin Island folks. Do not mix them up. I have learned to detect the proper accent, although before that would just not say a word. Lived in downtown Atlanta long enough to know silence is golden when placed before assumption.