Southerners registered to vote in the Republican primary as early as 76 would probably have been diehard partisans and unlikely to vote for Carter, extremely less likely IMO then registered Democrats in the south were to vote for Reagan in a general election.
Not all states had closed primaries. In fact, Reagan was actually doing better in open primaries.
The answer to this question is quite a few southerners, but I'm sure the voters existed in significant numbers everywhere except maybe New England.
