This thread is based on some stuff I read about the ideological evolution of the Democratic Party in Peter Beinart's, The Good Fight.
Beinart noted crucial events in '47 and '48. The Biltmore Conference, leading to making anticommmunism part of Democratic Party orthodoxy, Truman's support for a civil rights plank in '48, leading to the Dixiecrat rebellion. The ideological synthesis you ended up with was described by Arthur Schlesinger as "Vital Center" liberalism. It combined a desire for domestic reform with a forward policy abroad. Truman then proceeded into the 1948 election, winning a close victory, even while his ideological positions led to defection on the left (Wallace's Progressives) and on the right (Thurmond's Dixiecrats).
Truman's surprise victory in '48 vindicated Schlesengerian anticommunist liberalism. Truman did have an unhappy second term, but the ideology came back in, celebrated again, with JFK's victory. It did not unravel until the later Johnson years, under the strain of Vietnam and the New Left and resurgent right.
Stepping back again, how would Democratic Party ideology have been effected if Truman lost in '48 instead of winning?
Would later Democrats have absorbed the idea that either supporting containment of the USSR, or supporting black civil rights, or both, were automatic death to any Democratic political coalition?
Would the next winning Democrat have consequently been completely uninterested in confronting civil rights issues?
Would greater skepticism toward the Cold War have been a more mainstream position within the Democratic Party through the rest of the forties, fifties and sixties, instead of being eclipsed for all practical purposes between 1950 and 1965? Note that there was significant unease among many liberals about Truman's policies of supporting rightist Greek and Turkish regimes in '47.
Overall, do Doves and Dixiecrats gain in relative power?
In the ATL, you would not have the Democrats have the Korean War precedent of fighting an limited, executive war to further the containment doctrine. You may not have a Korean War, period, if Moscow, Beijing and Pyongyang interpret Dewey's policies in Asia differently than they interpreted Truman's in OTL.
Meanwhile, might the Vital Center ideology take up residence in Dewey's GOP? Where will his party stand on civil OTL's Truman and Eisenhower administrations? And what will his containment policy, both diplomatic and military, look like?