They’re often correlated, but one doesn’t arise out of the other. Us Bangladeshis have a strong tendency to blame our culture for what ails our country (our tendency to corruption, etc.) If an American said “I wouldn’t want mass immigration from Bangladesh to the US because of the prospect of cultural change” I’d probably be inclined to agree. My family left the country to get away from that culture. In Bangladesh it wouldn’t be a controversial statement to say that there are aspects of Chinese culture or whatever that we don’t like.
So when I see Trump attacked as “racist” I find it bizarre. His criticisms are plainly directed at culture, not race. For example his comment about “shit hole countries.” That’s a boorish phrasing of the situation, but it’s clearly an attack on culture, not race. If you asked a Bangladeshi on the street whether they’d rather have immigrants from they’d say something similar. The state of a country is a reflection of the culture of its people. It has nothing to do with race.
Weird, in my bubble (mostly college-educated, mostly urban-to-suburban, mostly liberal-to-progressive, though there are many exceptions on every axis), that wouldn’t even be a controversial statement (once you got into mechanisms of limitation and more specific cultural concerns such as what kind of drift you wanted to avoid, there would be debate, though, both over principles and pragmatics.)
> As far as I can tell, many American liberals think race and culture are the same thing
They aren’t the same thing, though they are (contrart to racist models) very closely related.
> I would have to go out of my way to find some evangelicals in the Deep South who won’t even discuss the idea and dismiss it as “blasphemy” or some such.
Huh, I can find plenty of college educated, urban California religious conservatives (not necessarily evangelicals) who see it that way without much effort. (Like, zero effort when I go to church.)