Celery is OK if you remove the strings we give our bunns celery all the time...Cabbage I am not certain about! Someone else could maybe jump in on that one!
You don't have to remove the 'strings' from celery if you cut it into small pieces. The 'strings' can get stuck in the throat so cutting the celery into small slices cuts those strings and eliminates the risk. Be careful though, feeding celery can have the same effect as iceburg lettuce if given too much so it should be fed sparingly.