You said the south was always a conservative stronghold. Yet some state went for Bryant with over 90% of the vote, Roosevelt with over 80% of the vote, and Carter with over 60% of the vote. The south was solidly Democrat until they realized they could switch to Republican and still keep their big government, big spending heritage.
Just in case you didn’t know, the democrat party used to be the conservative party and the party that supported less government and lower taxes. This changed over time, but it took many southerners (who had voted democrat all their lives) a number of years to realize this.