I don't really think that Arkansas is much less socially conservative than other Southern states outside the Deep South. Also, unlike Tenn., N.C., and Va., it doesn't have any liberal pockets. The fact that it is less Republican on the national level probably has more to do with economic liberalism and partisan politics.
The fact that there aren't any real liberal pockets - and the fact that there's a sizeable very Republican pocket - have a lot do with it, I suppose. Helps in painting the Reps as the party of wackos.
Yeah, it's pretty weird. Even in 2004, Dems took about 30% of the self-described born again Christian vote in the state. Elsewhere in the US, it's closer 10%, sometimes 15% (according to exit polls. In some states, the question is for White Conservative Protestant instead. Sorry, don't have a link).
I suppose that right at the time when most of the remaining social conservatives deserted the Democratic Party in the second half of the 90s, the US happened to have an Arkansas president who remained insanely popular in his homestate, even with social conservatives, and that by the time he was out of office, the realignment had essentially ended.
But Gustaf's point about a small suburban population is also important.