I did a clean instance just to eliminate any doubt. My actual pack uses REI instead of JEI, but that seems to have no bearing on this bug because the behavior is the same. Tested by simply copying and tweaking the zombie loot json to drop stone instead of zombie flesh and placing it in "kubejs/data/minecraft/loot_tables/entities/zombie.json on both the server and client. I will note that any script use to edit mob drops or villager trades through MoreJS will also have the same behavior, not just data "pack" loading.

Checking recipes for stone on client will show that zombies drop it, but when on a server with identical settings, it will show the unedited rotten flesh drop. Again, these were tested with clean instances with only the below mods and the zombie loot edit. Server was localhost.

MC: 1.20.1
Forge: 47.3.7
JEI: 15.12.3.55
JER: 1.4.0.247
kubejs: 2001.6.5
Architectuary: 9.2.14build14
rhino: 2001.2.3build6