WD40 is a mineral oil, and is "not a good thing" on any wood product. It's basically kerosine with some additives. Wiping the strings with a stick of warm butter would do less damage to the wood (not a recommended practice).

Mineral based "lubricants" are not generally compatible with vegetable (wood) parts. They generally will cause weakening/softening of the wood.

Vegetable lubricants nearly all harden - sooner or later - when exposed to air, and hence must be used with some caution and only in appropriate places.

Animal fats are mildly destructive to wood, but don't usually harden; hence the use in things like cork grease for the joints on your clarinet. They do eventually "change the woodiness" of even the cork - which isn't very "woody" to begin with.

I've been told, but haven't confirmed, that FastFret and similar products are basically a "silicone grease" which is an artificial product neither animal, vegetable, nor mineral in the usual sense. It may be assumed that the makers haven't been sued over their effects on instruments. Suit your own taste about using them, I suppose.

John