It is impossible to catch an unexpected RuntimeException from an ActionEvent in a generic way.
A customized response to that exceptions is impossible, which is critical for us because our application is a 24/7 app for a power plant control system.

Here is a sample app:
============================================
import java.lang.Thread.UncaughtExceptionHandler;
import javafx.animation.PauseTransition;
import javafx.application.Application;
import javafx.beans.property.IntegerProperty;
import javafx.beans.property.SimpleIntegerProperty;
import javafx.stage.Stage;
import javafx.util.Duration;

public class ListenerExceptionTest extends Application {

	@Override
	public void start(Stage stage) throws Exception {

		Thread.setDefaultUncaughtExceptionHandler(new UncaughtExceptionHandler() {
			@Override
			public void uncaughtException(Thread t, Throwable e) {
				System.out.println("Caught in DefaultUncaughtExceptionHandler: " + t + " " + e);
			}
		});

		IntegerProperty counter = new SimpleIntegerProperty(0);

		counter.addListener(o -> {
			throw new RuntimeException("Unexpected RuntimeException in InvalidationListener");
		});

		PauseTransition counterIncrement = new PauseTransition(Duration.seconds(1));
		try {
			counterIncrement.setOnFinished(e -> {
				counter.set(counter.get() + 1);
				counterIncrement.playFromStart();
				throw new RuntimeException("Unexpected RuntimeException in ActionEvent");
			});
		} catch (Exception e) {
			System.out.println("Caught from setOnFinished: " + e);
		}
		counterIncrement.playFromStart();

		stage.show();
	}

	public static void main(String[] args) {
		try {
			launch(args);
		} catch (Exception e) {
			System.out.println("Caught in main: " + e);
		}
	}

}
============================================

It results in:
============================================
Caught in DefaultUncaughtExceptionHandler: Thread[JavaFX Application Thread,5,main] java.lang.RuntimeException: Unexpected RuntimeException in InvalidationListener

java.lang.RuntimeException: Unexpected RuntimeException in ActionEvent
	at de.fhg.iwes.javafx.vpp.frontend.ListenerExceptionTest.lambda$1(ListenerExceptionTest.java:35)
	at de.fhg.iwes.javafx.vpp.frontend.ListenerExceptionTest$$Lambda$56/2077198483.handle(Unknown Source)
	at javafx.animation.Animation.impl_finished(Animation.java:1132)
	at javafx.animation.AnimationAccessorImpl.finished(AnimationAccessorImpl.java:49)
	at com.sun.scenario.animation.shared.SingleLoopClipEnvelope.timePulse(SingleLoopClipEnvelope.java:103)
	at javafx.animation.Animation.impl_timePulse(Animation.java:1102)
	at javafx.animation.Animation$1.lambda$timePulse$25(Animation.java:186)
	at javafx.animation.Animation$1$$Lambda$72/2057789281.run(Unknown Source)
	at java.security.AccessController.doPrivileged(Native Method)
	at javafx.animation.Animation$1.timePulse(Animation.java:185)
	at com.sun.scenario.animation.AbstractMasterTimer.timePulseImpl(AbstractMasterTimer.java:344)
	at com.sun.scenario.animation.AbstractMasterTimer$MainLoop.run(AbstractMasterTimer.java:267)
	at com.sun.javafx.tk.quantum.QuantumToolkit.pulse(QuantumToolkit.java:447)
	at com.sun.javafx.tk.quantum.QuantumToolkit.pulse(QuantumToolkit.java:431)
	at com.sun.javafx.tk.quantum.QuantumToolkit.lambda$runToolkit$363(QuantumToolkit.java:298)
	at com.sun.javafx.tk.quantum.QuantumToolkit$$Lambda$41/28432492.run(Unknown Source)
	at com.sun.glass.ui.InvokeLaterDispatcher$Future.run(InvokeLaterDispatcher.java:95)
	at com.sun.glass.ui.win.WinApplication._runLoop(Native Method)
	at com.sun.glass.ui.win.WinApplication.lambda$null$141(WinApplication.java:102)
	at com.sun.glass.ui.win.WinApplication$$Lambda$37/1109371569.run(Unknown Source)
	at java.lang.Thread.run(Thread.java:745)