Let me describe the first few words of Keynesian economics, Supply Side economics, Demand Side economics, Monetarism, and Welfarism.
"The government shall influence the economy by..."
Now let me describe the first few words of Free Market economics.
"The government does not influence the economy..."
We've had this argument about the word "Capitalism", which according to you is anything short of full Marxism. But you don't get to throw in government management of the economy with Free Market economics. There is no way to stretch that definition far enough. That's because all the rest are a direct violation of the definition of Free Market. You cannot have a term mean its opposite.
There are libertarians who favor abandoning the term "capitalism" and only using the term "free market" because there are those who overload the term "capitalism" to mean all of the above ideologies. But there is no way to justify overloading the term "free market" because its definition is much more explicit and it is the government doesn't try to stimulate demand, and it doesn't try to stimulate supply, and it doesn't manage the money supply, and it doesn't try to stimulate GDP, and it doesn't enact policies to distribute money to the poor, and it doesn't enact policies to distribute money to the rich. All of those policies, all of those ways that the government would try to do something with the economy (always with the best of intentions of course since I don't want to blaspheme your god) are against the very basic definition of Free Market.
No, they are not compatible with their opposite.