Manejar notificaciones push de Android sobre la actividad actual

Cree un receptor de transmisión local
Cuando reciba una notificación en FirebaseMessagingService, enviará los datos a la actividad que necesita con un LocalBroadcastReceiver. Es fácil y seguro.

En tu FirebaseMessagingService

@Override
public void onMessageReceived(@NonNull RemoteMessage remoteMessage) {
super.onMessageReceived(remoteMessage);

//Take the data from message received
String myData = remoteMessage.get("MyDataKey");

//Send data through a local broadcast receiver
Intent intent = new Intent("IntentFilterAction");
intent.putExtra("MyDataKey", myData);
LocalBroadcastManager.getInstance(this).sendBroadcast(intent);

En actividad onCreate

//Create BroadcastReceiver
BroadcastReceiver broadcastReceiver = new BroadcastReceiver(){
      @Override
      public void onReceive(Context context, Intent intent) {
          super.onReceive(context, intent);

          //Get data from intent
          String mydata = intent.getExtras
      }
};

IntentFilter intentFilter = new IntentFilter("IntentFilterAction");
LocalBroadcastManager.getInstance(getContext()).registerReceiver(broadcastReceiver, intentFilter);

En actividad en Destroy

//Unregister BroadcastReceiver
LocalBroadcastManager.getInstance(getContext()).unregisterReceiver(broadcastReceiver);

Espero eso ayude :)