ADDITIONAL SYSTEM INFORMATION :
This has happened continuously since at least JFX 11/Java 11, and continues in 14 (the latest I can test at the moment).

openjdk version "14.0.2" 2020-07-14
OpenJDK Runtime Environment (build 14.0.2+12)
OpenJDK 64-Bit Server VM (build 14.0.2+12, mixed mode)

I'm using openbox as a display manager. There are least two other reports across the internet: https://stackoverflow.com/questions/24519668/javafx-maximized-window-moves-if-dialog-shows-up
I've confirmed it doesn't happen on Windows.

A DESCRIPTION OF THE PROBLEM :
In a maximized window, if a button click causes a dialog to appear the parent window will be effectively un-maximized and moved halfway across the screen. The parent window remains this way after the dialog is closed.

STEPS TO FOLLOW TO REPRODUCE THE PROBLEM :
Run the code below and press the button

EXPECTED VERSUS ACTUAL BEHAVIOR :
EXPECTED -
Parent window should not move or stop being maximized
ACTUAL -
Parent window moves

---------- BEGIN SOURCE ----------
import javafx.application.Application;
import javafx.scene.Scene;
import javafx.scene.control.Alert;
import javafx.scene.control.Button;
import javafx.stage.Modality;
import javafx.stage.Stage;

public class App extends Application {
  public static void main(String[] argv) {
    launch(argv);
  }

  public void start(Stage stage) throws Exception {
    Button button = new Button();
    button.setOnAction(e -> {
      Alert alert = new Alert(Alert.AlertType.INFORMATION);
      alert.initOwner(stage);
      alert.initModality(Modality.WINDOW_MODAL);
      alert.show();
    });
    stage.setScene(new Scene(button));
    stage.setMaximized(true);
    stage.show();
  }
}
---------- END SOURCE ----------

FREQUENCY : always