Religious groups do charity work to get tax breaks. All of them.
Getting the tax breaks is not the real reason to engage in charity work. When an organisation collects millions from their members, certain part of that collection must be used to fund charity work but in reality, a huge chunk can be re-routed to certain individuals. By cooking the books, certain individuals having a hand in the charity will say the money is used for this and that charity but who knows?
As long as the members do not complain, all will be cosy and rosy. How do they know what amount is used for charity and how much is re-routed? It is more like pulling wool over the eyes of the members who are told their pastors are kind hearted souls. Just like the Madoff guy who could hoodwink investors for years because he was seen as a good investment banker on the surface but underneath that demeanour, he was just a crook.