Seems a bit odd for the government to benefit from not having to provide food or shelter to some people due to a community place of worship, and then deny that same place of worship needed aide.
In this case, I don't believe the government is "benefiting" from not providing food, shelter, etc. for Community A due to HoW assistance. There are budgets; money not used for Community A instead provides food, shelter, etc. for Community B. "I'd like assistance now because I let you rally on my lawn last year" seems silly. If the church helped Mr. Congressman rally, Mr. Congressman probably paid the church to use its property in the first place up front OR, when asked for assistance, wrote a personal check to the church instead of allocating government funds.
We should also ask the people in these communities what they're doing to give back to their HoWs. It's not the government's responsibility to bolster them because HoWs don't pay taxes. I have faith (no pun intended) that religious communities are strong and help their own. Say Mr. Construction Contractor's local church helped him garner funds to pay for his wife's life-saving surgery. He could "pay the church back" by donating workers, equipment, and/or time from his company in the wake of a natural disaster. Even someone who doesn't own a business like Mr. Construction Contractor and benefited from the church, like a patron of a soup kitchen, has two hands and can help do something
in the way of physical labor.
And, I may be wrong on this point, I don't assume that all individual church coffers are private -- it makes sense to me that churches would help each other out in times of need. Even if the coffers are individually private, wouldn't a Lutheran church in Iowa wire over some money or volunteers to help out a Lutheran church in New Jersey? Or what's stopping a Maine synagogue from helping a New York church? Or an atheist from helping a Connecticut mosque?
People help each other when they need it, especially when they've been helped reciprocally in the past.
What's stopping anyone
from helping anyone
when it's the right thing to do
I think it does a benevolent HoW a disservice to say that the government "owes" it anything and that it would fall into dissolution without FEMA aid. Plus, what's stopping someone from worshipping amongst white-washed walls instead of stained glass? Does it really matter? Will someone's god not listen to them because they're not in a pretty room?