> It seems wrong that faith-funded organizations are allowed to discriminate based on religious belief.
Not that I think it's morally acceptable for faith-funded charities to turn away some people based on their lack of faith, but:
a) Individuals acting on their own founded and run the organization. It would be a violation of several important rights (theirs) for a government to regulate how they choose to run their charity, or whom they choose to help.
b) I have a hunch that a lot of these anecdotes attribute discrimination incorrectly -- i.e. I suspect the person in question was more than "not a believer". People who get turned away because they're chronically abusing the system (or for similar reasons) tend to infer malice where there is none, and level accusations accordingly.
That being said, I strongly disagree with any open-to-the-public charitable organization discriminating on the basis of religion or any other categorization, beyond the "this person is abusing the system and we don't want to hurt them further by continuing to enable this destructive pattern in their life -- so we can't provide further X to them until they do Y and Z".