The easiest way is to create a local mod list identical to the server mod list. There is a simple way to do it and you will only need to log on your server once to take a “snapshot” of the mods.
Log on the desired server once. Log out.
Go to: \SteamLibrary\steamapps\common\Conan Exiles\ConanSandbox
Copy the file called servermodlist.txt (it is a temporary file updated when you connect to a modded server).
Paste the file in the folder called Mods in the same location. If you don’t have a folder, just create it.
In the Mods folder, rename the servermodlist.txt to modlist.txt.
NOTE: Your active local modlist will also be used when you log in a singleplayer game. If you want to use different mods for your singleplayer, just rename the modlist (e.g. modlist1) and create one for your singleplayer game.
An alternative solution is to take a snapshot of the server mod list and load them 1 by 1 in the same order in the main menu but this is usually much slower.