I am running SkypeForLinux on Debian Stretch with Cinnamon desktop. The Skype works fine when chatting with a group until I share my desktop. Once I share the desktop the audio quality degrades to the point that I can hear just rattling sounds when someone speaks. The Skype same time starts to display "Poor connection" message.
It cannot be a connection as I have symmetrical 300mbps fiber. This is my connection speed taken during one of the troubled calls: http://www.speedtest.net/result/7405654671
The hardware is much higher than one is required to run Skype:
CPU: Intel(R) Core(TM) i7-4710HQ CPU @ 2.50GHz x4
RAM: 12GB
SSD