I see a logged exception during the initial render of the example:

SEVERE: Exiting serializeView - Could not serialize state: java.lang.reflect.Field
java.io.NotSerializableException: java.lang.reflect.Field
at java.io.ObjectOutputStream.writeObject0(ObjectOutputStream.java:1164)
...

Looks like we store instances of java.lang.reflect.Field in a HashMap that isn't transient:

public class FilterTableBean extends BaseTableBean {

    private List unfilteredList;
    private Map columnFilterInput = new PutMonitoringStringHashMap();
    private Map columnFields = new HashMap();

MyFaces shows up this type of serialization problem quite early since, by default, it serializes the View to the session. This can be turned off with a configuration parameter but it would be a problem in any serialized situations (e.g. clustering) so should be addressed.

Other composite comps/examples that use the FilterTableBean will have the same issue.