I think it's unlikely it is mold.
More likely it is paraffin crystals forming from the type of oil that was used at some point on the slings.
I learned my hard lesson several years ago.
A write-up in Tactical Knives by a well respected writer said to soak old leather knife sheathes & handles in Thompson Water Seal wood sealant to stop decay in old leather.
So I did it to a WWII Kaybar handle & sheath, a Vietnam era jet pilots knife, a couple of new hand made sheaths I had made, and a Rusty Sherrick horsehide rifle sling.
That was probably 20 years ago.
And to this day they are still growing white paraffin crystals out of the Water-Seal treated leather!
Only way I have found to slow it down or semi-stop it for a few months is take it outside, buff off all the white grunge, and re-wax it with Kewi Clear shoe polish.
That lasts for 6 mo to a year.
Then you have to do a 'Do-Over' again!
rc