FWIW - Olive oil has been used on leather for thousands of years before neats foot oil was even thought of and is still used by many of the finest leather craftsmen working today. Based on intensive research by both myself and several other historical types, t he oldest date for neatsfoot oil usage we have been able to come up with was in the early 1700's and one of it's first usages was for fine gun oil and not for leather. Also outside of the Fiebings brand there is no traditionally made neats foot oil (made from the lower leg bones ans sometimes hooves of young cattle) that I am aware of - all other neatsfoot oil on the market today is processed from hog lard and has been so since the 1930's, just check out the MSDS...
I've used olive oil (Extra Virgin cold pressed only) for over 40 years and have never had it go rancid. As for mineral oil - I will have to respectfully disagree in part with Paul. I would say it depends on the quality of the mineral oil. Ballistol, for instance, is a highly refined water soluble mineral oil and I know many serious outdoor users who have used the stuff on my gear and love it and have reported excellent results with no downside after long time usage. Also IIRC Al Stohlman recommended using mineral oil at times (when prepping for dying?) - vet grade is another highly refined version and is available at most any farm/feed store.
With ANY oil the thing to remember is it can be over done, veg/bark tab leather should have about an oil content of between 18-22% max - beyond that it can and will cause damage via destruction of the cell walls - that's why over oiled leather is floppy...