From what I've seen, the type of oil in the a/c system HAS to be compatible with the type of refrigerant in the system or there might well be a resultant gel from the mixing of the oils that can settle out in the bottom of the condenser, thereby cutting down the effective size of the condenser with internal restrictions in the lower circuits.
When the whole R134a thing started initially, the recommendation was to put the R-12 recycling machine on "liquid" and flush the system to remove all of the residual oil. With that done, then the correct oil and new R134a was added.
Make sure that your replacement compressor has the same oil pan on it as the one that came on the vehicle. I believe there might be a "dipstick hole" on the compressor case (with a screw in plug in it) to check the oil level--once the refrigerant charge has been removed. Otherwise, the Chrylser service manual will have the recommended capacity listed.
In more modern times, a/c system oils are much more universal than they used to be, but unless you purge the whole system of any old oil, it might be best to keep using what's already in there than to put something else in there.
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