The problems, as I see it, are two-fold.

First, everyone thinks that churches doing charity is a great idea (because they tend to be darn good at it), and everyone thinks helping them is also a great idea -- provided you happen to approve of the church type. Almost no one wants the money to go to the XYZ Cult of the Satanic Transexual Aliens, and if you accept one religious belief over another, that's state-sponsored religion.

In short, "Yes, the money is great. Provided it only goes to MY church."

Second, once a church accepts federal money, they also have to listen to what the feds say about what to do with the money. Whether you like what particular church charity groups do or not with their money, do you really want the federal government to dictate your (or their) religious activities and how you adhere to your beliefs?

And if you let any church do whatever they want with tax money, then you are forcing people (namely taxpayers) to subsidize religious activity they don't agree in -- atheists paying to be support a God they don't believe in or Jews paying to support Jesus -- which violates the Constitutional right to freedom of religion.

Freedom of religion is just that -- freedom to or freedom from, you have it or you don't.