Example of an implementation for a custom TableHeaderRow with overridden showColumnMenu()

CustomTableHeaderRow.java

import javafx.collections.FXCollections;
import javafx.collections.ObservableList;
import javafx.geometry.Side;
import javafx.scene.Node;
import javafx.scene.control.ButtonType;
import javafx.scene.control.CheckBox;
import javafx.scene.control.ContextMenu;
import javafx.scene.control.Dialog;
import javafx.scene.control.MenuItem;
import javafx.scene.control.ScrollPane;
import javafx.scene.control.TableColumnBase;
import javafx.scene.control.TableView;
import javafx.scene.control.TreeTableView;
import javafx.scene.control.skin.TableHeaderRow;
import javafx.scene.control.skin.TableViewSkinBase;
import javafx.scene.input.MouseEvent;
import javafx.scene.layout.VBox;

public class CustomTableHeaderRow extends TableHeaderRow {

    private final TableViewSkinBase skin;

    public CustomTableHeaderRow(TableViewSkinBase skin) {
        super(skin);
        this.skin = skin;
    }

    @Override
    protected void showColumnMenu(MouseEvent mouseEvent) {
        VBox box = new VBox(5);
        ScrollPane pane = new ScrollPane(box);
        pane.setFitToWidth(true);

        // This would be easier with an interface or (abstract) class.
        ObservableList<? extends TableColumnBase<?, ?>> columns = FXCollections.emptyObservableList();
        if (skin.getSkinnable() instanceof TableView<?> tableView) {
            columns = tableView.getColumns();
        } else if (skin.getSkinnable() instanceof TreeTableView<?> treeTableView) {
            columns = treeTableView.getColumns();
        }

        for (TableColumnBase<?, ?> column : columns) {
            CheckBox checkBox = new CheckBox(column.getText());
            checkBox.selectedProperty().bindBidirectional(column.visibleProperty());

            box.getChildren().add(checkBox);
        }

        Dialog<Void> dialog = new Dialog<>();
        dialog.initOwner(getScene().getWindow());
        dialog.getDialogPane().setContent(pane);
        dialog.setTitle("Columns");
        dialog.getDialogPane().getButtonTypes().add(ButtonType.APPLY);
        dialog.show();

        // For a custom context menu
        ContextMenu contextMenu = new ContextMenu(new MenuItem("abc"));
        // Note: A bit inconvenient here: Target is either the cornerRegion or the 'image' StackPane, 
        // which is a children of the cornerRegion.
        Node target = (Node) mouseEvent.getTarget();
        contextMenu.show(target, Side.BOTTOM, 0, 0);
    }
}