If this is on XB1 with Kinect, the console (or more precisely: The Kinect and how it is setup to recognize and log XB1 users in) and not Destiny may the problem. If so, the friends app won't work either. In order to resolve this on XB1, power cycle the XB1 (press the power button for at least 5 seconds until the console powers down). Before powering the XB1 up, disconnect the Kinect. Then power the XB1 up. After that, the friends app and the fireteam functionality in Destiny should be working again. At that point of time, you should also be able to reconnect the Kinect to your XB1 (you may however also want to wait until you turn your console off again and reconnect the Kinect only before turning the XB1 on the next time). That's what worked for me when I encountered that problem.