ORA-04091:la tabella xx_xx sta mutando, il trigger/la funzione potrebbe non vederlo

Non puoi eseguire query su una tabella mutante nel trigger.
Vedi questo:https://docs.oracle.com/cd/B19306_01/appdev.102/b14251/adfns_triggers.htm

Prova invece questo codice:

create or replace 
TRIGGER log_changes 
  AFTER INSERT OR UPDATE OR DELETE
  ON passengerlist1
  FOR EACH ROW

DECLARE
 t_name varchar2(255);
 t_surname varchar2(255);
BEGIN
   IF DELETING THEN
    SELECT PERSON1.GIVENNAME, PERSON1.FAMILYNAME INTO T_NAME,  T_SURNAME
    FROM PERSON1
    WHERE PERSON1.PERSONID = :OLD.PERSONID;

    INSERT INTO LOGS VALUES (T_NAME, T_SURNAME, :OLD.FLIGHTID, SYSDATE);
   END IF;

   IF UPDATING OR INSERTING THEN

     SELECT PERSON1.GIVENNAME,  PERSON1.FAMILYNAME  INTO T_NAME, T_SURNAME 
     FROM PERSON1 
     WHERE PERSON1.PERSONID = :NEW.PERSONID;

     INSERT INTO LOGS VALUES (T_NAME, T_SURNAME, :NEW.FLIGHTID, SYSDATE);
   END IF;
END;
/