'Sure, you managed to make the game load and not crash, but now plug-in A's anti-dupe code is preventing Mod B's unique crafting mechanic from working, causing input items to be voided. They have a poor history of compatibility with other modding platforms you can usually get them to work (and I can think of about a half dozen over the years which promise they work great with Forge mods), but you almost always end up with weird and catastrophic bugs that come about from two completely different communities modifying the same base code and the vast majority of the two sides not talking to each other. However, we have a website to modify the configuration file online, you only need to import and modify your current configuration file. Those sound more like what you are looking for, but you won't find much help with them here. Unfortunately, there is no way to modify the CustomSkinLoader configuration file in the game currently, so you need to manually modify it by using a code editor (e.g. However, the separate community which focuses on vanilla-compatible server mods would be what we call Server Plug-ins.

If a Client has only Client-side mods then it should be able to join a vanilla Server just fine.

If a Server has only Server-side mods then vanilla Clients should be able to join just fine. Forge (and I assume Fabric) is designed to be usable by vanilla clients/servers.

Minecraft mods without forge