The Republicans were associated with Hoover, Depression, unemployment and reckless isolationism. Roosevelt had been President for 12 years and would have been President for more terms had he not died. Veterans were getting their college paid for and their home loans underwritten by the federal government. There was a fear of a postwar recession and a feeling that government spending could prevent it. Many who lived through the Depression would swear that they would never vote for another Republican ever. Friedrich Hayek's book "The Road to Serfdom" was greeted with abuse and catcalls.
There were real limits as to how conservative (in our current understanding of the word) any candidate could be in 1948. That's as true of Thurmond as of Dewey or Taft.
I don't buy that Thurmond in 1948 was the same as Goldwater or Reagan in later decades. Thurmond was another Democrat with Democrat ideas on business and government who had broken with the party over civil rights issues.
I suppose it's possible that had the Dixiecrats won -- something they themselves probably didn't consider possible -- government would have grown less than it did. Indeed, they opposed everything that would have weakened their position, including the later admission of Alaska and Hawaii as states, so it's not surprising that they would have blocked most new government programs -- not for philosophical reasons, but because they wanted to preserve segregation and weakening the federal government seemed to be the way to do this. There would have been some advantages to such a strategy.
But we would have had other serious problems. It's likely that our history would have been far more turbulent than it turned out to be. And it's also possible that, had civil rights been removed from the table, Thurmond would have been as supportive of government growth as any other Democrat. The Dixiecrats had been more or less loyal Democrats earlier and, but for the emergence of racial issues, they could easily have remained such.
Dewey was the conservative, prudent, and responsible choice that year. Of course he was a New Yorker, and hence, more liberal than most Republicans, but he wasn't really a Rockefeller type. Rockefeller really threw himself enthusiastically into big government liberal Republicanism. Dewey was more pragmatic and adaptable. He had to be more liberal to win in New York and would have been more conservative in the White House.