I'm from New Mexico (which I believe leans towards Hispanic/Latino majority, or at least pretty close to 50/50 Hispanic/non-Hispanic) so probably biased, but I always find that really weird, too. I do find that a lot of Americans in areas with less Hispanic influence do make a weird differentiation between being white and being Hispanic, but I find it odd for people who are presumably immersed in the culture to some degree just by virtue of having close connections to Hispanic people.

So I guess my answer would be that yes, a lot of Americans would differentiate between white and Hispanic in a racial sense, but they're also not really people who tend to be married to Hispanic people, if that makes sense? I think most people who have that kind of close connections to Hispanic culture would realize the variety there, and also realize that telling certain Hispanic people that they're not white are fighting words, lol.