ok, I admit it, I am anal. You were warned. If a hide is oily first thing I do is figure out why. if the answer is it wasn't well scraped (often the case when buying something unusual that was part of an aviary etc) I scrape it down to skin. then I wash it, with the gentlest stuff that will do the job. Frequently this is a bit of simple green and water- especially with poorly scraped hides. once it is washed I blot it (not rub like you would hair- just press down with dry cloths and lift) then dry the feathers with a hair drier so they go back to looking like feathers should. once this is done, I peg the skin out on a board hide side up using thumb tacks, and use either Borax (heavy oil from very poor scraping) salt (just a bit of scraping needed pretty well done mostly- this is the case with some whiting I purchased in the past.) or corn meal (very light oiliness left skin was properly scraped but perhaps not soon enough) Borax I find is much more likely to cause a very dry paper like skin that will potentially tear, so I do not use that on a previously treated hide unless it really soaked up a good deal of oil. salt is a mid point, it does dry the hide and draws a good deal of oil out and a few days under a good layer of salt is sometimes just what a hide needs. Corn meal is good for when there doesn't seem to be a good reason for where the oil is coming from. I can tell you from experience that if you slaughter more today than you can clean, scrape, wash, treat, peg out and borax, that after a nice hot July evening when you get to them tomorrow a great deal of the fat that needs to be scraped from the skin has melted and seemingly coated the skin, chances are that a good deal of it is in the skin and will slowly come out making your feathers oily without there being a good reason that's obvious. No one ever plans on having to process a hide the next day, but too often odd things happen like ones son falling out of a tree and breaking his arm resulting in being at the hospital from 3pm till after 11pm. Honey do's are often another issue. I also find a few of these in 'commercial' hides, and I assume that they for one reason or another just sat longer than is good. (should be noted that when I am slaughtering and processing the hides, I slaughter, process the hide, slaughter the next and so on so I never have to deal with more than one of these.)
There is a fascinating paper titled "Feather mites play a role in cleaning host feathers: New insights from DNA metabarcoding and microscopy" by Jorge Dona, et al That looks at the gut contents of feather mites and identifies what they eat. it most appears to be bacteria that live on feathers and in the oils of feathers. it also appears that the mites are not what damages the feathers (quote: " in spite of using primers suitable for amplifying degraded bird DNA. We observed no obvious feather filaments in our microscopy analysis, but this and our molecular study would not have been able to identify tiny (non-DNA-bearing) fragments of feathers, which have been occasionally reported in microscopy studies. The chelicerae of vane-dwelling feather mites do not seem capable of cutting or tearing intact feathers, so if the tiny fragments we observed in the guts are indeed feather fragments, they would likely be ingested along with other loose material. In addition, we found a high prevalence of both keratinophilic and pathogenic fungal taxa") Now what this means in a nutshell is that even if a feather collection is mite free, it can still be damaged by bacteria that can live in the oils. This of course requires that they somehow are introduced (or perhaps survive processing?) If there is a 'rancid' smell then there is likely some sort of bacterial action, is it a harmful taxa? I couldn't say, but decided fairly quickly I dislike the idea and do try to keep my collection as free from possible food sources of bacteria as possible which does mean removing any excessive oils.
you were warned...
Added: be aware you can not, should not and must not remove all oil from feathers or they will be damaged. Only try to do more than simply wash them if there is for some reason excessive oil in the attached skin that is leeching out onto the feathers. The oil present in a properly cleaned and processed hide is not enough to host an invading colony of destructive bacteria, its not a reason for concern, the process in effect preserves the hide to a large degree, proving that bacterial action is not a major concern. the only time to be concerned is when there is excessive oil present, unpleasant odor or visual confirmation of bacterial/fungal infestation of the hide. so a tiny bit of oil- if it bothers you, wash them and blow dry them.