The public and protected "show" and "hide" methods (and related methods like showAndWait, setShowing, close, etc) of Window, Control, and Skin, including their subclasses, should throw an IllegalStageException if called on a thread other than the FX app thread. Some of them already do, but many do not, which can lead to unpredictable failures at runtime. See JDK-8349004 and JDK-8349096 for an example.

Most JavaFX objects, such as Node and Scene, can be constructed and modified on any thread unless and until that object is attached to a visible Window. Showing or hiding a Window is an operation that must always be done on the JavaFX application thread as documented in the Window and Stage classes.

The PopupWindow class defines additional show methods that are not documented to throw an exception, but in the cases where they do actually show the window, they will get an exception. Similarly the ContextMenu subclass of PopupWindow defines two more show methods with the same problem.

Some controls and skins also have operations that will show or hide a popup window. As with the above methods in PopupWindow, some operations can fail, often in hard-to-detect ways, if called on the wrong thread.

Here is the list of classes whose show and hide methods (and similar) should be documented to throw an exception if called on a thread other than the JavaFX Application Thread, and this restriction should be enforced at runtime:

Window subclasses:

javafx.stage.Window
    javafx.stage.Stage
    javafx.stage.PopupWindow
        javafx.scene.control.ContextMenu

* Control subclasses

javafx.scene.control.ChoiceBox
javafx.scene.control.ComboBoxBase
javafx.scene.control.Dialog
javafx.scene.control.Menu
javafx.scene.control.MenuButton

* Skin subclasses

javafx.scene.control.skin.ComboBoxBaseSkin
    javafx.scene.control.skin.ComboBoxPopupControl
        javafx.scene.control.skin.ColorPickerSkin
        javafx.scene.control.skin.DatePickerSkin