That's usually handled by the individual HUD's display conditions.
E.g. if you've set up an In Menu game state (usually set up by default), your HUDs can depend on that and decide if shown or not.
You can also add a more exact control over when to display what via adding your own game states (that are not set automatically) or using variable conditions in your HUDs. Menu screens (and other parts) can use schematics to enable/disable stuff as needed.
