^I dug up the most R/D congressional threads:
https://uselectionatlas.org/FORUM/index.php?topic=186234.0
https://uselectionatlas.org/FORUM/index.php?topic=186775.0
And most of the states that have white majority D areas are going to be states with very little minority areas anyway. ME, NH, VT, ID, WY, UT, probably IA (though not 100% sure). That Alaska district is majority native Alaskan though. Minnesota, Oregon, Washington, and Montana will probably have majority white D districts (MT and OR don't have election data, unfortunately) too.
To comment on Arkansas, I was surprised to see how Republican the northern end of Lonoke County is. Its consistently ~78% McCain. I didn't even try to pull one in the NW, but someone could try.
I checked Iowa and that Des Moines district was ~55% white. An Iowa City-Cedar Rapids district is almost as Democratic, but >80% white.
You don't need Cedar Rapids. Staying within Iowa City one can make a SD with 75.4% Obama and 82.8% WVAP.