Tung oil comes from a Chinese nut and people who are allergic or sensitive to nuts/nut oils should avoid contact with tung oil or any product containing tung oil - like peanuts, the vapors alone can cause an allergic reaction/attack.
I don't claim to be an expert on tung oil but after a few bad experiences of my own, I've done considerable research and some experimentation.
If you see "Polymerized tung oil finish", "tung wiping oil finish", "Tung oil gloss", "Danish tung oil", "Swedish oil" or anything similar in name, more than likely it will not be any good for exterior or gun applications. The "finish" products are often blended with varnish, rosin and/or wax(es) in order to obtain a product that's cheap to make and easy to use but it's not true tung oil nor will it be anywhere near as durable. There are a few tung oil blends sold for exterior applications but chalking, peeling, blistering and cracking are issues with these products commonly reported by boat owners. The particular product I had cracking & peeling issues with was "Minwax Tung oil finish" - I learned the hard way after putting it on a shotgun stock, went on easy and dried very fast, half a dozen coats gave a very nice shine with minimal finishing & buffing. Within a few days of carrying the gun hunting, the finish was already starting to wear off and by the end of small game season in the areas where the finish wasn't worn off, it was all check-cracked.
A process called polymerization is used to intensify Tung Oil's natural cross- bonding tendency - this process is slow and requires tightly controlled heating of the oil, too hot and it plasticizes or burns, too cool and it doesn't polymerize. Heat polymerizing does darken the oil and the extent to which it has been taken in temperature and time as well as the properties of the particular oil itself can result in the oil being anywhere from tea colored to nearly a black tar. Tung oil that is properly heat polymerized will require considerable thinning before use, usually 2:1 to 4:1 thinner to oil - the type of thinner used will have a proportional effect on the drying time but even if using naphtha the drying time for pure polymerized tung oil is usually not less than 36 hours. In my trials, the very dark heat polymerized tung oil thinned 4:1 with naphtha and applied moderately (enough to see the oil lay on top of the wood but not enough for it to be runny) the first coat penetrates quickly but will remain sticky to the touch for about 24 hours. On plain un-stained maple, it will impart a color ranging from honey amber to a light brown, the more coats applied, the darker the color will get. Leaving the sample blocks out in the weather, sun & rain, water beaded and ran off and the wood appeared to be damaged over about two months of continuous exposure. Tung oil properly polymerized using only heat will produce the hardest finish
The word "finish" is usually what gives away that "polymerized tung oil" is not just oil. Because the polymerization process is time consuming and expensive, companies simply blend tung oil with varnish and other additives rather than cooking it. The result is that it will not withstand exposure. Other tip-offs that the product is not acceptable for use on gun stocks or anything else associated with exterior use: "not for wood floors", "not for food preparation surfaces", "not food grade", "gloss", "high sheen", "no buffing required" are just a few of them. Pure tung oil (drying agents & thinners don't make it un-pure) will not dry to a gloss finish, it has to be rubbed and it will still not reach a full gloss look.
"Fast drying" does not necessarily mean that tung oil isn't pure nor does it mean the oil is not blended with other finish materials like varnish but I have noticed that the faster the oil dries, the less penetration depth it achieves and the surface will not dry completely smooth. Too much drying agent will result in the finish being brittle, it won't have the same amount of "give" as do slower drying mixtures. Pure tung oil most forgiving when it comes to dents & dings, as long as the drier content was not too high the finish will not normally crack or split even with severe deformation of the wood.
The easiest way to avoid problems is to request an MSDS for the particular product. Most times the ingredients will be listed only by CAS or UN numbers but these can be quickly found on-line and if the ingredients contain anything other than tung oil, a drying agent and solvent, I'd avoid using it on anything intended for outdoor use.