Hello Rome. Thanks for the nice words and concern for my safety!
In the specific case of these rifles the red stripe was placed on the stock by the Brits to differentiate its caliber, .30-06, from their .303 chambered Enfields. These rifles are in near mint condition with the exception of the dings on the stocks and perfectly safe to shoot. I put 10-20 rounds through it after cleaning. On the left side of the stock within the red area is either a stenciled 30 or 300 (varies on some rifles) to further emphasize the caliber difference.

I should have added some more of the gun's background in my post. Remington got a contract in 1941 to produce the 1903 rifle. Roughly 55-60,000 of their early production line went to the U.K. The Brits apparently didn't do much with them as evidenced by their excellent condition.
The USAF gent that I mentioned bought a fair number of crates (12 rifles to a crate) directly from the Briish Ministry of Defense for pennies on the dollar. A few crates were consigned to a U.S. museum/ gunshop in the late '90s, and some but not all were sold in private transactions. The remainder including my rifle were still in unopened crates until very recently. I heard about these over on the surplusrifle forum (U.S. Military Rifles). The original buyer has passed on and a nephew now has the remaining crates.

Over a period of time Remington gained approval to make various mods to its production line, ultimately resulting in the 03A3. What has puzzled collectors is the lack of documentation on the considerable number of mods, timing, when approved, etc. Remington produced a fair number of 1903s, so in and of itself, they are not rare. What is unique about these "red stripers" is that they came back to the U.S. (legally) without import stamps and in near mint condition sans the dings and dents on the stocks then remained sealed in their wooden crates for 40 plus years until the 90s. Some crates have yet to be opened according to the source.

Hope this explains things a tad better.
Regards
Bob