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)