ArcGIS Pro crashes when projecting through a Clickshare device.
This crash is not due to a defect in ArcGIS Pro. The crash occurs due to DLL injection by the Clickshare driver. DLL Injection is a way for advanced programs to load their own code into another application’s address space. The crash occurs in DXCap64.dll - the Clickshare capture driver. This is why it is only reproducible when using the Barco Clickshare device.
Esri corresponded with Barco Support and their recommended workaround is to disable DLL injection by setting an environment variable, see the Barco technical article: Can I Turn off DLL injection?