The application hangs when you click on a Label element placed in the DropDownContent of RadSplitButton. In order to recreate this the content of the Label should contain an underscore character, thus enabling the access text WPF functionality. Also, the CloseOnPopupMouseLeftButtonUp property should be set to True.
This behavior can be reproduced with any element that is not derived from FrameworkElement. The issue in this case appear because when the access text is enabled, the Label control produces Run elements in its visual tree. The Run class doesn't derive from FrameworkElement, but from FrameworkContentElement, which causes the issue.
To work this around, use TextBlock instead of Label.