I’m sure more knowledgeable people can explain more thoroughly, but I’ll give it a go 
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To the best of my knowledge you have to have the exact same mod list, in the exact same order as the server - if they don’t have a particular mod (even just HUD mods), then afaik it won’t work.
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Yep, you’ll need to swap them out - fortunately it’s not particularly difficult - they don’t need to be uninstalled, just removed from the active modlist (this is somewhere I’m more confident - while I don’t play on servers, I do frequently swap modlists in and out):
from the game’s main menu screen, just click on ‘Mods’ - from there you can link to the workshop if there’s any particular mods you want to subscribe to. All mods you are subscribed to will appear in the left hand column. To add a mod to your ‘active’ list, simply select it in that left side box and click the arrow between the two boxes to move that mod across into the centre box. Mods within that centre box can be shifted up and down in the order by similarly selecting the mod and then clicking arrows to move it up or down the list (I find it helps to hit ‘refresh’ at the bottom of the screen before re-ordering the mod list, otherwise it doesn’t always seem to take).
Once you’ve got your modlist in the order you want, clicking ‘back’ will tell you you need to restart the game for changes to be applied. Do that and you should have all your selected mods up and running.
To remove mods from the list is exactly the same thing - just select it in the middle box and hit the arrow to shift it back to the left box.
- really not my area - hopefully someone else can help here - my guess would be that it should be as simple as both the server and the client having the exact same modlist in the exact same order. But there may be more to it than that, I don’t know.
Hope that helps for a starter 