Update 0.10.0.0 will have Steam rich presence support according to Trello. Could there be a setting to disable this? Steam itself doesn’t provide an option other than to hide that you’re playing anything at all, and that’s going too far.
If disabled, it would still show your server or current activity to any of your friends in the main menu, and to others on the same server via the tab player list just as it does right now.
Pinging @Sketchman as the weekly update topic indicates you might be the best person to suggest this to.