Mad Max 1 showed a society in collapse. They still had production capability at that point, so only scarcity was a problem for fuel.
In Mad Max 2, Lord Humungus was attacking a pumping & refining station to be able to acquire more fuel. Again, easily explained & consistent.
In Mad Max 3, most of the fuel was gas. Specifically methane & byproducts, produced from biowaste. Again, easily explained in-universe.
In the newest Mad Max, they speak of a "gas town" with which they trade water for fuel. Gas town is probably a pumping station & refining capability. I'm not a particular fan of the latter, but it's explained in-story once again.
As for realistic fuel post-apoc? You can run an engine on a huge amount of types of fuel. From wood (yes,
wood), over coal & alcohol to nuclear power.
The question is, what resources and knowhow will be available in your specific post-apocalyptic setting?