I despise rattles too!
I have neoprene 1/8" rubber liner inside the cabinet drawers (self adhesive on one side, so we just cut and inserted). We've gone through several different sets of cutlery (metal, plastic, and one-time-use), but now carry 4 of these:
https://www.amazon.com/Portable-Uten...LPPPD_BwE&th=1
We also bought some steak knives so we have one in each case (the knives included in the set serve purpose for most everything except gilled steak)
There are many variations available with similar sets, I just prefer the cloth style bag over a hard case (less likely to make noise), and the handles on the ends of ours are larger than what most offer.
You could just use an organizer style bag and accomplish the same (once it's rolled up and tied off it will keep everything from making any noise (had something similar originally, but found having the 4 separate cases more convenient - YMMV):
https://www.amazon.com/PWPAM-Camping...1&sr=8-24&th=1
EDIT - for quick & simple fix you could always just rubber band each set - would minimize most of the noise.