Oklahoma has historically had a super-closed Republican primary, and has been as safe a Republican state as one could get since 1952. Yet, Republicans only exceeded Democrats in party registration there at some point in 2014. In 1960, 82% of its voters were registered Democrats. Not even FDR in 1932 ever got over 75% of Oklahoma’s vote. Only one Democratic House candidate in 1932 got higher than 82% of the vote (and the district he represented almost certainly had an even higher proportion of registered Democrats). So far as I can tell, the lopsided Democratic registration advantage was due to the primary once being tantamount to election for many local offices, thus resulting in the Oklahoma Democrats not being an organized political party until after the Gingrich revolution.
Lesson: elections are one thing. Party registration is quite another.