Not an expert, but if you read any of Keynes, he's basically critiquing classical economics and pointing out some of the ways it fails to explain economic cycles, hence the invention of macroeconomics.
Really? Classical liberal economics fails to explain business cycles? Then why is the Austrian School (dyed in the wool classical liberals) the only major economic faction that's developed the most comprehensive expose on how central banks cause malinvestment, booms and busts by fiddling with the money supply?
I don't think most Austrian econmists would self-identify as neoliberals. Politically they tend to be Libertarians (in the U.S.) or free market anarchists or minarchists (or I suppose laissez faire). Basically free-market instead of stat interventions. I belive most neoliberals quite readily accept state interventions, central banking etc.
The core tenent is that the free market is the best allocator of factors of production and entrepreneurial profit is the guiding factor. The state tends to interfere with this. It's best summarized in the socialist calculation debate.
However, there's also basically a split (mostly reconciled these days) betwen a more Hayekian wing which is more accepting of the mainstream (and could possibly self-identify as neoliberals) and the state in general and a wing that is more in the spirit of von Mises.
Disclaimer: just interested in the history of economics, not an economist.
You're a bit mistaken. Austrians are basically anti-statists who believe in limited government and non-intervention in the market - even to the point of opposing legal tender laws.
Keynes has to be THE most confusing and self-contradictory personality in orthodox economics. He had no original insights and the only reason political elites took a liking to him was because he gave them a logical, complicated copout for money printer to go brrrrrrr. He frequently changed his theories and ideas for political expediency and the idea that modern 'economists' take his teaching as gospel truth is just sad.
Murray Rothbard wrote an entire profile on the man [0] and I'd suggest anybody taking a stab at heterodox economics to read it.
I'd rather have some Keynes than get pissed on with some 'trickle down' economics.
I would say, I'd bet nobody having an argument about economics here has actually read much Keynes, or anything about classical/neo-liberalism. It all just turns into "I recognize some word related to the right, so I'll virtue signal and keep hyping it." Or more, "I see a free market economy argument happening, I must jump in and comment because markets are from God and I must support".
When dealing with Marxist or Keynsians (or modern monetary theorists for that matter) it is a safe bet that the people implementing the policies haven't read and don't intend to follow the theory.
So I am simultaneously shy of saying "Kaynes was wrong" and confident that anyone claiming "Kaynes was right and we must do suchandsuch!" is saying the wrong thing. Ditto the other theories.
https://en.wikipedia.org/wiki/Austrian_business_cycle_theory