Bubbled up on SO https://stackoverflow.com/a/61539677/203657 - copied the example here for convenience.

To reproduce, run open popup and click on menuItem
- expected: new root showing without errors
- actual: new root showing, NPE in MenuButtonSkin

Exception in thread "JavaFX Application Thread" java.lang.NullPointerException
    at java.base/java.util.Objects.requireNonNull(Objects.java:222)
    at javafx.controls/javafx.scene.control.skin.MenuButtonSkinBase.lambda$new$7(MenuButtonSkinBase.java:198)
    at javafx.graphics/com.sun.javafx.application.PlatformImpl.lambda$runLater$10(PlatformImpl.java:428)
    at java.base/java.security.AccessController.doPrivileged(AccessController.java:391)
    at javafx.graphics/com.sun.javafx.application.PlatformImpl.lambda$runLater$11(PlatformImpl.java:427)
    at javafx.graphics/com.sun.glass.ui.InvokeLaterDispatcher$Future.run(InvokeLaterDispatcher.java:96)
    at javafx.graphics/com.sun.glass.ui.win.WinApplication._runLoop(Native Method)
    at javafx.graphics/com.sun.glass.ui.win.WinApplication.lambda$runLoop$3(WinApplication.java:174)
    at java.base/java.lang.Thread.run(Thread.java:832)

The example:

import javafx.application.Application;
import javafx.scene.Scene;
import javafx.scene.control.Label;
import javafx.scene.control.MenuButton;
import javafx.scene.control.MenuItem;
import javafx.scene.layout.StackPane;
import javafx.stage.Stage;

public class Main extends Application {

  @Override
  public void start(Stage primaryStage) {
    MenuButton btn = new MenuButton("Switch...");

    MenuItem item = new MenuItem("To 'Hello, World!'");
    item.setOnAction(
        e -> {
          StackPane root = new StackPane(new Label("Hello, World!"));
          primaryStage.getScene().setRoot(root);
        });
    btn.getItems().add(item);

    primaryStage.setScene(new Scene(new StackPane(btn), 500, 300));
    primaryStage.show();
  }
}

Converted into a unit test:

    @Test
    public void testMenuButtonSkinNPEOnReplaceSceneOpenPopup() {
        MenuButton menuButton = new MenuButton("switch");
        MenuItem menuItem = new MenuItem("Press '_a'");
        menuButton.getItems().add(menuItem);

        Scene scene = new Scene(menuButton);
        Stage stage = new Stage();
        menuItem.setOnAction(e -> {
            StackPane root = new StackPane(new Label("Hello, World!"));
            scene.setRoot(root);
        });
        stage.setScene(scene);
        stage.show();
        menuButton.requestFocus();
        menuButton.show();
        assertTrue("sanity:", menuButton.isShowing());
        assertSame(scene.getFocusOwner(), menuButton);
        
        // trying to see the NPE
        // working options (the exact sequence of events is slightly different)
        // keyboard on menuItem and press accelerator
        KeyEventFirer keyboard = new KeyEventFirer(menuItem, scene);
        keyboard.doKeyPress(KeyCode.A, KeyModifier.ALT);
    }
    
The error happens in the showingListener installed in skin:

            if (popup.isShowing()) {
                boolean showMnemonics = NodeHelper.isShowMnemonics(getSkinnable());
                Utils.addMnemonics(popup, getSkinnable().getScene(), showMnemonics, mnemonics);
            } else {
                // we wrap this in a runLater so that mnemonics are not removed
                // before all key events are fired (because KEY_PRESSED might have
                // been used to hide the menu, but KEY_TYPED and KEY_RELEASED
                // events are still to be fired, and shouldn't miss out on going
                // through the mnemonics code (especially in case they should be
                // consumed to prevent them being used elsewhere).
                // See JDK-8090026 for more detail.
>>>> the scene here might be null
                Scene scene = getSkinnable().getScene();
                List<Mnemonic> mnemonicsToRemove = new ArrayList<>(mnemonics);
                mnemonics.clear();
>>>> that's why we get the npe here
                Platform.runLater(() -> mnemonicsToRemove.forEach(scene::removeMnemonic));

Note that this is a different root than the other NPEs (JDK-8244081, JDK-8244110) around MenuButtonSkin, it's uneffected by cleaning up in the sceneListener and/or in dispose. There seem to be several paths that remove the accelerators from the scene, probably need to find them all and guard against null (or funnel into a single cleanup, don't know if that's possible)