It would be really appreciated if you turned kinect off, especially if you're already using a mic. No one is interested in hearing domestics, your wife or kids nagging you to spend some time with them, babies crying, feedback echos and a whole host of other nonsense. If like me, you're relatively new to the game and didn't realise the game automatically opts to use kinect as a mic, then it does.
Add to that, I'm sure you yourself don't want all your business being aired over open chat. Some of the stuff you hear I can only assume is meant to remain personal.