I very, strongly recommend against using Neat's foot oil, or Mink oil. It's about like using WD-40 on a handgun, and leather professionals will yell at you just as loudly if you use them as gun professionals do when WD-40 is encountered.
What you don't believe me?
http://www.indygear.com/
It's a site devoted to Indianna Jones "gear" so to speak. Indy uses a lot of leather (the whip, the jacket, the shoes/boots) and various members of the above website have had the opportunity to talk with a Mr David Morgan, the top dog in the world of whip making. He strongly, and ONLY recommends the use of Pecards Leather Dressing:
http://www.pecard.com/
I've used the stuff on the Indiana Jones shoes/boots (most I ever paid for a pair of shoes), jacket and whip, and anything else I own that's leather (don't own anything suede). Keeps the rain off, and if you ever get any scratches, rubbing this stuff on'em makes'em disappear. Can't comment on rifle slings... but they do have a section for Equestrian products (saddles, etc.) which might be a slightly more appropriate blend.
The stuff works miracles. Wanna impress the ladies? Take a pair of their old leather shoes, and apply Pecards Leather Dressing. Make's their shoes look (almost) brand spanking new. I should really take some pictures.
Safe to use with your fingers too.
Don't work for'em just very impressed with'em.
-Morgan