I know that Skype is not part of Office Insider, but after the last update - version 2103 (Build 13827.20004) - Skype will no longer open. Skype's splash screen briefly appears then Skype quits. Event Viewer has the entry Faulting module path:
Apologies for the late response. We believe this should have been resolved in the latest Beta channel update version 2103 (Build 13901.20036). Please let us know if you are still experiencing this after installing that build.