Here's a link to an interesting article in the Wall Street Journal about what the writer calls a "Backlash Against Tithing". People seem to be reacting to some of the extravagant spending of churches and want more accountability. If that is the case for churches it is certainly even more so for other not-for-profits.
Jesus not only advocated for tithing he seemed to indicate that the tithe was just the start and we really should give more than the tithe of 10% of our gross income, and to do it out of joy and not legalism or obligation. He said in Matthew 23:23, "Woe to you, teachers of the law and Pharisees, you hypocrites! You give a tenth of your spices--mint, dill and cummin. But you have neglected the more important matters of the law--justice, mercy and faithfulness. You should have practiced the latter, without neglecting the former."
Of course, that doesn't preclude fiscal responsibility and accountability. Anytime we are asking people to release their hard earned resources for our cause, and I think especially when it is the work of God's kingdom, we should expect the utmost transparency and integrity.