You are completely right about the Soest crossbow, this was the one I meant.
Nevertheless, we know many paintings with white, unvarnished crossbow tillers and arquebuses. I am conviced that in times of war, wood on weapons was only meant to survive for few days or weeks, at best. Then the stocks were broken at best and replaced. Even in Thirty Yeras War paintings, we notice white stocks on both matchlock and wheellock guns. I guess, due to their quick consumption they were just not worth staining.
In my collection, a ca. 1645 Austrian matchlock musket is preserved with white (now heavily patinated) beechwood stock. It came from the Styrian castle of Schloss Frondsberg, from where about 15 similar muskets were sold via Tom Del Mar a couple of years ago, all in the same untouched condition with rust patinated iron parts and unstained stocks, with all the traces of original carving still visible.
A few images attached.
What's even more, I own the earliest known completelety preserved gun in the world, High Gothic, ca. 1400, the lock mechnism and hook being working time alterations of ca. 1430. Its crude oak stock much resembles a compemporary crossbow tiller (!), it is of heavily patinated brownish gray surface and shows no traces of staining whatsoever.
Remember: crosssbow bolts (quarrels) were an absolute mass production and certainly not stained originally - and look at their dark colored oak or ash surfaces now!
As to limewood, it is not only soft and easy to carve but at the same time very tough. As I mentioned various times, most early 16th c. arquebus stocks were made of limewood, as their very special scent of incense denotes.