I can see the motivation. Sure it sounds horrible at first blush. But consider the religious issue a little closer.
As catholics, we are called to serve the poor. Why? I would propose that the reason we are called to do so is only tertiarily (did I make that up?) to meet the physical needs of the impoverished.
The PRIMARY purpose to for the needy person to experience the love of Christ in the giver. The secondary purpose is for the giver to encounter Christ in the poor person.
When christian charity organizations lose their particular identity as a Christ-centered outreach, most of the point has been lost. I’ve SEEN this first-hand. I’ve done short term youth ministry in dozens of parishes, rebuilt homes in urban Chicago, and been on diocesan poverty fighting mission trips in third world countries. Time and again, I’ve seen that when the ENTIRE team is motivated to do what they do out of love for Christ, incredible things happen. When the team loses critical mass and there are enough people there for the still noble, but secularized goal of providing for the needy, things fall apart and the organization gradually becomes no more effective than a government program.
When it is the real thing, the ENTIRE team prays together (absolutely including janitors and truck drivers), serves together, sacrifices together and winds up meeting Jesus together. Truly an awesome thing to behold.
I don’t know this group nor if the above is what they are thinking. But it is a possible explanation for the policy. I’m sure there are many out there who would howl that such a group should be banned from receiving tax money. I think this is shortsighted. Religious groups that have a universally acknowledged public service as A goal (not necessarily their entire set of goals) SHOULD still be eligible for tax money as long as that portion of their mission that is secular is achieved as efficiently or better than a purely secular group does it. (And naturally, I think this should apply to schools too, but that’s another can of worms…)