Stay logged into the game and go afk when you have to leave, so no one knows if you're actually on or not unless they look at the list.

In seriousness I don't understand why they have this feature without being able to be silenced. In my fc which is comprised of friends, no more then 20, it's not very annoying. But when I started the game and we were in a fairly big fc.... The chat log tbh was kinda annoying when people logged in and out.