To reproduce:

1. Right-click on the password field;
2. Pop-up and context menu will both appear.

import javafx.application.Application;
import javafx.event.EventHandler;
import javafx.scene.Scene;
import javafx.scene.control.ContextMenu;
import javafx.scene.control.MenuItem;
import javafx.scene.control.PasswordField;
import javafx.scene.input.ContextMenuEvent;
import javafx.scene.layout.HBox;
import javafx.stage.Stage;

public class BugPasswordFieldContextMenu extends Application {

    PasswordField testedControl;

    @Override
    public void start(Stage stage) {

        testedControl = new PasswordField();

        final ContextMenu contextMenu = new ContextMenu();
        for (int i = 0; i < 3; i++) {
            contextMenu.getItems().add(new MenuItem("Menu item - " + i));
        }

        testedControl.setOnContextMenuRequested(new EventHandler<ContextMenuEvent>() {
            @Override
            public void handle(ContextMenuEvent t) {
                contextMenu.show(testedControl, t.getScreenX(), t.getScreenY());
            }
        });

        HBox root = new HBox(20d);
        root.getChildren().add(testedControl);

        Scene scene = new Scene(root, 300, 250);

        stage.setScene(scene);
        stage.setTitle(System.getProperty("java.runtime.version") + "; " + System.getProperty("javafx.runtime.version"));
        stage.show();
    }

    public static void main(String[] args) {
        launch(args);
    }
}