Combining QQuickWidget and QGLWidget in the same layout causes rendering problems

We have QQuickWidget and QGLWidget in the same layout in the same layout position. Their visibility is handled with show() and hide() calls. When showing QQuickWidget or resizing the window the result is invalid: QQuickWidget might be black, it might contain the whole window layout or it is rendered upside down with wrong color etc.

The attached example (qt5-quick-gl-test.zip) demonstrates the problem. Try clicking the buttons and resizing the window. The outcome is one of the listed above.