This is a lttle bit of an old thread but I was also taught to stay away from olive oil on something that would reside in your saddle room because of rats and mice. I have used it with decent success on items that were more human used in nature, such as holsters, knife sheaths, notebooks, briefcases and etc. Old lessons die hard and the old fellas taught me or it seems that I remember maybe disproportionately maybe, to not use food based oils on tack items. As I think about it now, it is probably just so much hooey, does a hungry mouse really care if it is neatsfoot compound, neatsfoot oil, or olive oil slathered on the saddle skirt he's looking at? Like a previous poster said, it may well be the salt from the sweat. Things you hear from guys you admire coming up in this leather fascination thing tend to stick in your mind.
One thing I have been using for many years, and don't see much about on this or other boards, is jojoba oil. A guy who used to braid a lot of rawhide got me a quart of it maybe 15 years ago, he was working at the time on a starve-out ranch in the Gila Bend, AZ area. That is where these things grow wild, and some people have also taken to semi-farming them also for the oil.
The neat thing about jojoba oil is it doesn't ever get rancid, a lttle goes a long ways, but it is quite expensive. I wouldn't bother putting it on new items necessarily, but for rejuvenating old saddle leather, it is the best thing I have found. I bought another quart about three years ago and still have about half of that. It can be mixed with neatsfoot oil too to stretch it if need be. I use very light coats and sometimes use a hair dryer on low to speed up the soak-in. Like I say, just sitting in the shop, the three year old shop still smells fresh, you could fry an egg in it and be happy about eating it. Of course, the vermin probably like it too. LOL