In addition to their position that pastors who apostatised during the persecutions should not be able to administer the sacraments, the Donatists also held (along with the Novatians of the previous century) to the view that pastors should lead holy lives (per I Timothy 3:1-7) and that a man who was unholy in his conduct had no place in the ministry.
If the churches had listened to (and continued to listen to) what the Bible had to say, instead of to the extra-biblical arguments of a heretic like Augustine, we might not have nearly the issue with clergy child-abuse as we have now.