A friend gave me a sample of a common waterproofing/ moisturizing/ protectant containing equal parts boiled linseed oil, beeswax, and turpentine, which makes a paste.
Is there danger of the rags used to apply this combusting?
I would think not, since the oil doesn't seem to need to dry-- the paste/wax is usually heated with a hair dryer/ heat gun to cause it to absorb into the cloth or wood to which it's applied, and the rags simply have a paste residue, but better safe than sorry.
You have more or less answered your own question at the end: "Better safe than sorry." Treat the rags as potentially combustible. Spontaneous combustion is not caused by drying per se, but by heat generated by oxidation of the oil, which occurs during drying, and can be sped up by so-called drying agents. The boiled linseed oil remains subject to exothermic oxidation after combining. If the turpentine is a mineral-oil based product, it isn't subject to spontaneous exothermic oxidation itself, but it could still act to speed up the process in the linseed oil. If it's real turpentine, derived from distilling pine, it's also a risk.
In my shop, all rags with oil residues are considered potentially dangerous and handled appropriately (which for me means, if I think I might want to re-use the rag, hanging it so that it dries in a single layer with good circulation, so no heat build up can occur, and if not, tossing into the woodstove, where combustion is not a problem). I know it's overkill - most of them contain mineral products only, and won't spontaneously ignite, but, as you said, better safe than sorry, and by making it a rule and habit, I reduce the risk of an overlooked truly dangerous situation slipping through.
You very much want to err on the side of caution here.
Is there danger of the rags used to apply this combusting?
Yes.
All commercial finishing products containing boiled linseed oil have a safety warning similar to that given with straight boiled linseed oil, about the potential for spontaneous combustion in any rags contaminated with the product1.
This is true even when there's a relatively small amount of BLO in the original mixture, and/or when the mixture contains wax.
Dry the rags flat on the floor or draped in a single layer over the back of a chair, a railing etc. until noticeably stiffened. After this they are safe to dispose of in your domestic waste.
I would think not, since the oil doesn't seem to need to dry
Assuming you don't use the product up quickly enough that this is avoided you'll see that the mixture in the container will skin over, the top surface becoming kind of leathery2.
This shows clearly that even in a mixture such as this the drying oil component stays true to its nature, polymerising in the presence of oxygen, and it is this oxidation that can lead to fires.
1 Note that this means both the application and wiping off rags/paper towels, so even a relatively small amount in the cloth/paper is considered potentially hazardous.
2 I saw this in my homemade oil & wax finish made with food-grade walnut oil, and walnut oil has a noticeably lower drying potential than even raw linseed oil.
