Apparently people who think there is such a thing as neoliberalism and neoconservatism do not understand what classic liberalism and conservatism are.
Classic liberals (e.g., John Sturart Mill and Adam Smith) were in favor of maximum liberty. So, in the economic sphere, governments should not interfere in the market by enacting regulations that limit the liberty of capitalists to make money. Adam Smith proposed laissez-faire capitalism where humans act out of rational self-interest and the market produces the best outcomes. The problem with this philosophy is that when humans act solely out of self-interest, the result is: "greed is good" (Gordon Gekko in the movie "Wall Street") and, "selfishness is a virtue" (Ayn Rand, the high priestess of laissez-faire capitalism).
The notion that the invisible hand of the market will produce the best outcomes is bunk. Alan Greenspan (a devotee of Ayn Rand) testified before Congress after the economic meltdown in 2008. He was asked why the invisible hand of the market did not prevent the irrational greed on Wall Street that caused the housing bubble in the first place. He could have said: greed is good. He could have said that the business cycle (booms followed by busts) is inevitable under capitalism. What he did say is that "there must be a flaw in the theory." A FLAW? Is the pope Catholic?
Classic conservatives (e.g., Edmund Burke) were appalled by the excesses of the French Revolution where the mob chopped off the heads of the king and aristocrats because they were privileged by birth and took land away from the Church and divided it up among themselves because the Church told them that if you are poor this is the will of God and kings rule by Divine Right of Kings. The French Revolution was a Marxist Revolution of class warfare before Marx was born. Burke was a conservative because he wanted to conserve the ancient regime where kings were chosen by God and the Church told the people to be happy with their lot in life because their reward is in heaven (this is why Marx called religion the opiate of the people).
Since classic conservatives wanted to limit liberty (especially the liberty of the mob to destroy the monarchy and set up a republic in France), John Stuart Mill said of conservatives: "I never meant to say all conservatives are stupid. I meant to say stupid people are usually conservative."
So, when a politician today talks about free trade and conserving what existed in the past (America was great when it was the dominant power on the earth and taxes were low and there were no government regulations of the free market), they are classic liberals and conservatives, not neoliberals and neoconservatives. FDR was a neoliberal because unlike Mill and Smtih, FDR wanted to use the federal government to limit the liberty of the wealthy to amass great wealth and to tax them to enact social welfare programs that benefit the poor (e.g., Social Security). Neoconservatives want the US to intervene in the world unlike classic conservatives who were isolationist because they opposed entry of the US into WWI and WWII, until Japan bombed Pearl Harbor. Perhaps if there had been neoconservatives in 1932, somebody would have whacked Hitler and prevented WWII and the Holocaust.