When people talk politics, they talk about "the left" and "the right" as the two main factions, but there are actually four main political quadrants: the left, liberals, conservatives, and the right. The left and liberals are not necessarily the same, and the right and conservatives are not necessarily the same either. Those groups tend to form coalitions in their respective parties, Democrat and Republican, but there are stark differences between them.
The left is more of a Marxist philosophy, whereas liberals are more of a libertarian/classical liberalism philosophy who believe in free speech and basic individual rights. The left is more authoritarian, condoning the use of government power to enact socialism, communism, and progressive causes at the expense of classical liberal rights and individual freedoms.
The right is a philosophy based on hierarchy and using government power to create order in society, which could mean curtailing many liberal rights and individual freedoms. Whereas the conservatives are more about conserving the ways of the past—which sometimes include right-wing order and hierarchy, but other times conserving the ways of the past are liberal practices—even progressive causes of the left.
This is why there's somewhat of a consensus between liberals and conservatives—center-left and center-right—because most conservatives are trying to conserve classical liberalism. On the left there is a bit of a fracturing as the leftists take over the Democratic party through illiberalism. The true liberals are being driven from the Democratic party coalition and being forced to become Republicans, or independents, or Libertarians to maintain their classical liberal values. So the Republican party has mostly become classical liberals, neoliberals, and neoconservatives, which are ultimately quite similar. Meanwhile the true right wing are considered outcasts by the Republican party establishment. The neoconservatives and neoliberals in the Republican party try to gate-keep the true right from attaining any political power.
This is why neoliberalism is taking over the world: because neoliberals still hold power in the Democratic party, plus they hold power in the Republican party. Even though there is a growing leftist coalition, the neoliberals (like Obama, Clinton, Pelosi) are using them to increase their own power. The Republican party has also been overtaken by neoliberals/neoconservatives (like Bush, McConnell, Graham). So the Republican party and Democratic party are essentially the same thing, at least the establishments of each party. They differ only on certain social issues, with the neoliberal Democrats being more woke and the neoconservative Republicans being more Christian.
The epitome of this neoliberal-con uniparty can be represented in the Democrats by Hillary Clinton and the Republicans by Nikki Haley. They essentially have all the same policies except on certain social issues, like abortion and sex stuff, with the Clinton Democrats being woke and the Haley Republicans being anti-woke. But as for foreign policy, economic policy, and everything other than culture war issues, they are all the same. This is why Dick Cheany endorsed Kamala Harris.
Then there is the elephant in the room—or the elephant in the “elephant party”: Donald Trump. There is this great fear of Trump from the left, liberals, and neoconservatives alike--that Trump is some far-right authoritarian fascist--but he's really not very right-wing at all when you consider the true right. Many on the right support Trump, hoping him to be more of a true right-wing leader, but he's closer to a classical liberal. However, he also has certain "America First" policies that aren't identical to the establishment: his anti-globalist and anti-war policies, which would actually help the American working class. These America First policies are truly different from the neoliberal and neoconservative establishment in both the Democratic and Republican parties, which is why the establishment from both sides continues to attack Trump. They mask it all in this hysteria over Trump being this far-right threat, but he's not truly right-wing.
However, there is a growing movement on the true right, and we are likely to see a true right-wing leader sometime in the near future. How the left and neoliberal/conservative establishment reacts to that will be… interesting to say the least. Like the boy who cried wolf too many times, no one will listen to their screeching about fascists when one finally comes to power.