100% And I know from personal experience -- and yes, this is anecdotal -- that upon taking urgent calls like this, we have made sure that the connection to Manos de Cristo happened in real time, and that the need was met. We also have an emergency "pastoral benevolence fund" that the pastor can tap for just this sort of real and urgent need. I wish we were bigger/had more volunteer time and resources to make such things available, but we're also practical -- we are functionally a suburban church in a pretty well-off neighborhood. There aren't many folks in urgent need showing up at our door. BUT, we also work closely with a sister church, located downtown, that absolutely DOES face regularly urgent needs, so we make sure they are regularly stocked (my wife and I will be delivering some stuff this weekend, as a matter of fact).
Maybe my only point is that there are some intelligent logistics and practicalities involved -- a suburban church probably isn't going to keep a dozen cans of formula on hand. A church in a lower income area, or a mission project of multiple churches (e.g., Manos) absolutely does.
That is indeed illuminating, and not surprising. In my experience with inter-faith work, both catholic and muslim congregations regularly "walk the walk." Have any other issues with them that you want, but in terms of "God calls us to tend to the needy," they are often at the front of the pack.
Also not surprising. Perspective. Reminds me of the Eddie Izzard routine about how churches of one of the most oppressed populations nonetheless have some of the most joyous music and worship. That's because they know well the joy of simply having "enough," when you have been missing "enough" in recent memory.
The response of the more well-to-do protestant (and non-denominational - you should be skeptical of anyplace that calls itself a "bible church") churches is disappointing and also quite unsurprising.