Yea; considering the 357 magnum didn't get introduced until 1934, I'd say that there isn't a lot proof about what was acceptable 125 years ago.
Now; having said that, I believe that with the proper 357 magnum ammo, in a rifle, it can be very effective on white tail deer out to 100 yards. Their 180 grain out of an 18" carbine will go more than 1800 fps and 1300ft/lbs. At 100 yards, it's still around 1500 fps and 900 ft/lbs. The 158 grain is 200 fps faster. In my 24" octagon Rossi lever action, with the 180 grain, I can get right at 2000 fps and about 1600 ft/lbs out of the barrel. "According to my chrono on speed and some math". At 100 yards, I'm still getting around 1600 fps and 1000 ft/lbs. That's with 180 grain LFN.
There is absolutely nothing wrong with deer hunting whitetail or mule at that distance with that ammo. Anyone who says differently simply is living in the past and is trying to compare traditional handgun 357 mag ammo out of a 3-4" barrel. They simply don't know what's available and they are using bad data. Most states that allow deer hunting with handgun calibers like the 357 magnum, for humane kills, require a minimum of 500 ft/lbs remaining energy at 100 yards. BuffaloBore in a 24" has twice that at 100 yards. Even in an 18" barrel it's close to 900 ft/lbs. Speed and weight formulate energy. On a white tail deer, I'd feel comfortable with anything 750 ft/lbs or more at 100 yards. For mule deer, I'd want 900-1000 ft/lbs at 100 yards. I wouldn't shoot any of them past 100 yards. Plus, I don't scope lever actions, so 100 yards is about the end of my accuracy range with open sites for hunting. Target shooting I can go further.
Anyway; if you use ammo like BuffaloBore for hunting, then it's fine to use a 357 magnum to 100 yards. I'd use the 180 grain because it's solid. Their 158 grain is a hollow point. Still effective, just that I prefer the lead flat nose. If you use traditional handgun cowboy or personal defense ammo, then you have no business out there deer hunting.