You'll find a lot of the above comments condensed and resolved or corrected in Bob Flexnor's book, Understanding Wood Finishing. The table on Page 84 is one I refer to for information about oils. For protection he says pure Tung Oil is poor until you get to 5 or more coats, with sanding required between coats to produce a satin sheen. It's plus side is that it penetrates deeply. It's downside is that it is softer and slower to cure than BLO, with several days or a week needed between coats.
LO and BLO, on the other hand, are rated poor for protection in any quantity. Anyone who's had water marks on a linseed oil finished stock knows it picks water up easily. It's the Hoppe's #9 of wood finishes: the smell brings back great memories, but its function is outclassed by more modern formulations.
Tung oil finishes—as opposed to tung oil itself—are finishes that look like a tung oil finish when they are done, but need have no actual tung oil in them at all. It's a marketing gimmick in a sense.
Polymerized oils are oils that have been heated to hot oven temperatures in an oxygen-free atmosphere and held there to react for awhile. This causes polymeric molecular cross-linking to occur. Cross linking is why a resin hardens and becomes strong during drying, but air drying randomly makes some molecules cross-link longer and stronger than others, leaving more and less water resistant spots, while pre-cross linking by heat guarantees a minimum dried molecular length for greater strength and for consistent water resistance. This also leaves less additional cross-linking to be done by curing, so it speeds drying up. The downside is the faster drying means penetration is only medium, so the finish is nearer the surface. The finish is glossy.
Flexnor says Birchwood Casey Tru-oil is a polymerized oil. Polymerized oils provide good protection if they are built up. I do not, however, know how the less deep penetrating and quicker drying properties may interact with different stains.
Danish Oil is an Oil-Varnish finish. These finishes provide medium level protection, between linseed and polymerized oil. They can be had either glossy or flat and with and without stain built-in.
Wiping varnish is another good protection level product if built up. A lot of the "tung oil finishes" are this variety. It's cheaper than polymerized oil and doesn't dry quite as fast, but is still fast enough that its penetration, like polymerized oil, is only medium. However, flattening additives can give you the option of a flat finish, where polymerized oils are glossy. Examples would by Watco Wipe-OnPoly, Val Oil, and Fornby's Tung Oil Finish.
Stain interaction requires testing. Just remove the gun from the stock and test patches inside the barrel channel or the receiver inletting or under the butt plate. Somewhere it can't be seen later.