What you're talking about is Dixiecrats, not neocons. Dixiecrats were conservative Democrats who broke with their party when it was hijacked by the radical Left, particularly on racial issues. Strom Thurmond would be a case in point.
Neoconservatives were former leftists (in some cases New Deal liberals, in some cases outright Marxists) who were anti-Soviet, and those who followed in their footsteps. They retain many of their old leftist ideals, from support for the welfare state to Wilsonian foreign policy to liberal immigration law.
Neoconservatism is an intellectual movement born in the 1960s inside the monthly review Commentary. Commentary is the journal of the American Jewish Committee, which replaced the Contemporary Jewish Record in 1945.[1][2] On the "theoretical" side of neoconservatism, most influential neoconservatives such as Norman Podhoretz and his son John, Irving Kristol and his son William, Donald Kagan, Paul Wolfowitz, and Abram Schulsky, refer explicitly to the ideas in the philosophy of Leo Strauss.[3] They often describe themselves as "Straussians."