The DC-8 always had turbo-compressors for cabin air and had no direct engine bleed capability into the cabin. I remember being surprised when the B707 which had turbo-compressors added capability for direct engine bleed air to the air conditioning. I was bemused to read here that the C-130 uses engine bleed air for cabin use. The Electra with similar Allison 501D engines had two mechanically driven cabin compressors. When you pulled the 5th and 10th stage surge bleed valves on the engines to check the engine compressor blades you found the blades were often coated with oily residue. Having an oil operated prop in front of the engine air inlet will do that although some may have come from engine seals. We had to do a lot of compressor cleaning to maintain engine power and I think it was best not to breath that air too.
The CL-44 also had a mechanically driven cabin compressors, big old Roots blowers. The L-1011 used engine bleed air for the cabin but the APU drove a separate load compressor for pneumatics supply so any APU engine seal leakage would not have gotten into the cabin air.
Mention was made of deicing fluid. Had several instances where the APU was being used for keeping the pax comfy while deicing and fluid ran into the APU air intakes (or pneumatic air intake on L-1011) and caused bad fume problems in the cabin. We found that using the APU only for electrics still could get anti-ice fluid residue left in in there and it was best to clean it out by starting the engines off the APU before using it for air conditioning.
Synthetic jet engine oil is nasty stuff and any mechanic doing oil screens or gearbox work can tell you of the skin condition of his hands after a good soak in it.
I think the B787 use of separate compressors, electric in this case or of turbo-compressors as in the old days is the way to go.