American Politics as Libertarians vs. Populists

Maybe you could have LBJ not sign the Civil Rights Act or something and have the Democrats gain the support of social conservatives outside the south by being extra christiany. Combine this with an anti-war paleoconservative Republican candidate in '68 who's pro civil-rights and socially liberal and the counter-culture might end up economically conservative. With Republican big money allied with a socially liberal cultural movement you'd probably have a much more socially liberal America today, as long as we don't end up ruled by a populist junta.
 
No FDR. The Depression drags on and the major political divide is Coolidge-style "libertarians" versus Huey Long-style populists.
The problem with that scenario is that it probably results in an equal chance for Norman Thomas getting elected President in 36, in which case there still would be a socially liberal, economically left-wing political grouping, and thus a high probability that the opposition becomes pro-free market (at least in name) and socially conservative.
 
Top