I'd say there are four kinds of third party voters: 1) the ideological, 2) the disaffected, who are fed up with both major parties, 3) the distressed, who are responding to hard times or a crisis, and 4) special interest voters, who are usually voting for a sectional interest, but who in other countries vote their religion, or ethnicity or class or occupation.
Those who always want to vote for the most rightward or leftward candidate, the most "conservative" or the most "progressive" alternative fit in category #1. Single issue voters either fall under #1 or #4. Voters swayed by personalities usually fit in category #2. They may not know that they are disillusioned with politics as usual until the right candidate comes along, but afterwards they're sure. Yankee reformist, "good government" or "clean government" types usually belong in category #2. A lot of the support for Eugene McCarthy or John Anderson, Perot or McCain was of this sort, and not really ideological. The distressed voters (#3) showed up during the Populist movement and the Depression. Maybe some George Wallace voters fit in this category as well. We need category #4 to account for the Dixiecrats. Some Populists and "Farmer-Labor" types also fit into these category.
In Mississippi and South Carolina, the Dixiecrats were the local Democratic machine. They broke with Truman over his timid support of civil rights. Otherwise, they would have voted for him (though perhaps they'd oppose other measures of his in Congress). I don't think they had any conception or intention of winning. They just wanted to keep Truman from winning those electoral votes. Opposition to civil rights was always their main focus, though some people will try to gloss this over today.
Outside the South there was virtually no support for Thurmond and Wright. Only crackpots like Murray Rothbard supported the State's Rights Democratic Party. That Rothbard's view has attracted some support is a sign that people today understand the 1940s as little as Rothbard did. The political situation, possibilities, and the available options were very different then. Rothbard's method is usually to exclude what people thought and said at the time and recast the historical situation in terms of his own preoccupations. More on the Dixiecrats.
Counterfactual questions: What if Dewey had won? Would anything have been different? What if the Dixiecrats suceeded in preventing either candidate from winning a majority of the electoral vote and the House of Representatives had to decide the election? What if FDR had lived? Would he have been able to keep his coalition together? And what if Eisenhower had run as a Republican (or as a Democrat)?