Never use linseed oil that isn't actually proper BLO as you'll get mould on the stock. BLO is actually AFAIR slightly more changed than just by being boiled. But as it is called BLO most think it is linseed oil that has simply been heated and brought to boiling. It isn't!
"Boiled" linseed oil, nowadays, is raw linseed oil that has been treated with "dryers", metallic accelerators which speed up the oxidation process that turns the oil into a polymer. It was originally made, not exactly by boiling it, but heating it and even bubbling air through it, to start the reaction with oxygen.
Taken to it's extreme, linseed oil is also the basis of Linoleum floor coverings, basically solid oxidised linseed oil. In many ways still superior to modern vinyl flooring.
The raw oil takes longer to harden, but the net result is identical. The difference is that the "boiled" stuff still contains the metallic compounds, so is not considered food safe, or suitable for use on small children's furniture. Possibly that might retard mould growth, but if you are keeping rifles in an environment (very high humidity) where mould is a concern, you should also be concerned about rust. Or your storage methods in general. Of course concerns over toxicity are irrelevant for gun stock finishes.
The correct original treatment for e.g. Le Enfield battle rifles, is a 50-50 mix of turpentine and linseed oil. In wartime, "boiled" linseed oil was used to speed up the process. The generally beech wood stocks are very dense, so penetration of the oil needs some assistance, hence the turpentine thinner.
The turpentine is a solvent which thins the oil, helps it penetrate, then evaporates, whilst sucking it in to the wood structure, rather than just laying on the surface. Natural turpentine, and raw linseed oil are readily available and not expensive.
The purest linseed oil, and turpentine, has been the basis of artists oil paints for many hundreds of years, some still glorious after all this time, with little yellowing, the paint being mostly ground up pigments. Though when applied as a protective varnish afterwards, can yellow and darken, over hundreds of years, hence picture restoration.
The other natural oils that can be used are mostly nut based. Tung and Walnut for example. I use ordinary cooking walnut oil on my walnut stocks, it is a slow process, rubbed in by hand, a week or more between coats, but gives pleasing results. It also darkens a little, which I think enhances the result without resorting to traditional stains, e.g. Alkanet root. I have experimented by mixing it up with turps (not turps substitute) and Japanese dryers to turn it into something like the commercial walnut stock preparations, but find that, if you have time, that's not necessary and gives a nicer result.
Linseed oil finishes are correct, I think, for rifles of this era, however not the best for actual waterproofing, or durability. They do help keep the wood stable in varying humidity, and properly used can penetrate deep into the wood. And build up over many applications into a superb traditional finish.
For a wooden stocked rifle, to be used in all conditions, with a durable and easily repairable finish, still allowing dents and dings to be steamed out, a more modern concoction might be superior. However I am a bit old fashioned, so reluctant to change.
This is not necessarily the approach best used for fine cabinet work. Or things like fine boardroom tables, where spillages of alcohol, water, or damp hot coffee mugs or tea cups may be expected to occur.
So, in summary, I would simply suggest a 50:50 mix of raw linseed oil, and genuine turpentine.
Some further reading, FWIW:
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they do a wax which is brilliant. 
