Humphrey had a higher margin of victory in some rural outer South counties. Some examples...
Elliot County, KY:
D+37.4 in 1960
D+39.9 in 1968
Coal County, OK:
D+11.0 in 1960
D+13.1 in 1968
Mason County, KY:
R+15.8 in 1960
D+1.7 in 1968
Anti-Catholicism at play maybe?
I’d think so. As evidence, Menifee County, Kentucky, was carried by McGovern in 1972 by about nine points, but voted for Hoover in 1928 (one of only three occasions any of Kentucky’s eight McGovern counties went Republican before 2000) by seven votes. Floyd County, which McGovern won by 10 points, Smith only won by 5 points. Logan County, West Virginia, was the only county in that state to vote for McGovern, but also went for Hoover in 1928. So even if muted by unionisation, there was some anti-Catholic sentiment in coal country.