It should work the same as any other mutation.

Hmm, that's odd. It should be functioning fine.

The problem is with the Speedrun!! mutation.
https://steamhost.cn/steamcommunity_com/sharedfiles/filedetails/?id=128428347&searchtext=

Whenever I start it from a lobby with a local server, the cvars get reset to their default values.
It prints this message to the console:
FCVAR_CHEAT cvars reverted to defaults.
(Not sure if it's referring to the server or client side though)

I just gave it a test, and I didn't notice any issues. That message you posted above never showed in the console for me, and I played it from the main-menu selecting a Local Server.

Weird, I've tried clearing the config, validating the cache and disabling all other addons, and it still behaves the same way.

Set "sv_cheats 0" in the lobby before you launch the game. It's possible that you have cheats on beforehand, and when your server starts it decides to turn cheats off which will cause the cvars to revert to their original values.

That worked, thanks Kerry.

I noticed a related issue: If you start a lobby game, and then try to switch on cheats in-game, the same thing happens, and the convar list gets reset.