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.