I see the Christian doctrine as oriented towards the least among us Whether charity is dispensed throught churches or welfare departments makes no difference. You see it as a left- right issue apparently. I do not.Ignore for the moment all the theological discussion that Jesus's followers, presumably in a position to understand what he said - or we could hardly call him a good teacher - describing the faith otherwise, and whose actions cannot remotely be interpreted as "let's make the government, if not the Romans then at least the Jewish authorities, act in a socialist way. That's our mission."
Let's play along. What if there were an entirely non-religious network of folks. Imagine them as loosely-organised, motivated by some general desire to help others in an overall way. They live among us and meet semi-regularly, reinforcing some values of wanting to not only keep the poor from starvation, but help people find jobs, give them advice, set an example, help even the less-poor, or people who have other problems besides food.
There are problems for the recipients with this. They feel embarrassed or thought-less-of. The help is unreliable. Busybodies snake in. You get cut off if people feel you spent the last money on stupid stuff, or didn't make an effort on the job they found you.
Contrast this with a system where people are sent checks by a remote federal government because by law, they deserve them. Anyone who has dealt with those receiving government checks can tell you that this can erode even good character. Listening to people complain about checks that haven't arrived, or benefits that were cut off, or things they feel they should have, does not inspire compassion for the poor. It inspires contempt, because mostly encounter the ruined ones, not the decent ones. But what we expect, we come to feel we deserve. Just human nature. And we feel we have earned things that we really haven't, like Social Security. Plus, you get more crime concentrated around housing for the poor, with no way of getting out of the neighborhood unless you give up your subsidy. And you still have busybodies. But at least no one tells you what to do with some aspects of your life, and you don't have to go to any public place to be looked over at tut-tutted at. You're a free American, and no one will tell you to stop drinking or using drugs. No one will tell you that your choice of men is ruining your life. You will get badgered about nutrition classes and birth-control, and asked a lot of questions about your family-and-partner history, which will be stored on a government computer forever. But they mean well.
Let me head off the arguments right away that 1) the churches didn't take care of the poor adequately, which is why the government had to step in. We have the same percentage of poor people. The major driver for reducing poverty has been technological improvement, like rural electrification and cheap cars. And 2) that most people are on welfare very temporarily. I'm not just talking about welfare, but even if I were, it is also true that most people were only on private charity for a brief time.
Let's let those societies play out independently in our minds for a bit. Do the work yourself here. Think of examples in history where the various methods have been tried. (That is not entirely a set-up question. While I have a favored answer here, the results are mixed, and that is also instructive.)
Update: I forgot to mention, there is also a very different effect on the givers.
See also one of my favorite articles on charity