Non-rocket scientist here. Why would some oils being burned off the chamber walls during firing be a concern?
It isn't just the rocket chamber but practically all those parts, in which oxygen, temperature and pressure are in the right mixture to permit such contaminations to start a fire. Imagine for example a valve that is eroded and damaged by such combustions. Or a seal, that gets temperatures that it can not withstand.
Next, even at much lower temperatures, fat and oxygen can result in nasty corrosive acids. You could also have moisture in a cryogen line, for example in real rockets, that plugs valves and pipes. In liquid oxygen pumps, cavitation can actually result in ice forming on the pump impeller.
Finally, once you have the temperatures high enough at the surface eroded, even the most oxygen resistant metal will eventually start to burn itself. The Russians mastered oxygen rich preburner technology, but that does not mean that their engines are oxygen fire-proof, it simply has different temperature limits that can be prevented.