Rear End Grease and Manual Transmission Grease

I have been considering changing the rear end grease in my 57' Skyliner. I have read over the years how the modern GL-5 80w90 grease can damage older rear ends and transmissions. I also have a fleet of older cars and have been wondering what rear end grease should be used in our older vehicles in the rear ends and transmissions to avoid damaging them. Are there any recommendations of what should be used and not damage our older transmissions and rear ends which may have, for example, bronze parts? Also, if there is a recommendation, would the grease be readily available such as at a Napa store? Any pointers would be appreciated.

I doubt if you would have a problem with the modern grease it is probably better than it was years ago, I use Tractor Supply brand 80w90 in my cars and I never have had any problems.