You offer two reasons (though really it's three.)
The first is that if the government helps people (provides material support, in your phrase), it harms those people.
Is this true? It's quite possibly true sometimes,. But is it true by and large? You haven't offered any evidence, and I'm not convinced that there is any. In any case, when the government doesn't help people it's at least as plausible that at least some of the time, that results in harm. So even if both policies sometimes harm some people, that doesn't tell us which is worse.
But there's another problem internal to your argument. You're in favor of various kinds of aid, so long as it's not provided by the government. Presumably you're in favor of that at least partly because you think it can actually do good. But if private charity can do good and help people, it's not obvious that having the help come from the government can't do likewise.
Now there are questions here that philosophy alone can't answer: which kinds of aid programs, public or private, are most effective? And are they better or worse than no aid at all? Those are empirical questions. My admittedly non-expert reading of the evidence is that both sorts of aid can be beneficial and often are. But in any case, if one kind can be, it would be odd if the other couldn't.
You give another argument: public aid amounts to establishment of a state religion. However, all you offer in defense of this is an assertion: helping people in need is fundamentally a religious directive.
Why should we believe that? There are moral arguments for helping other people, but it's either arbitrary stipulation or confusion to claim that moral considerations automatically count as religious. And even if someone wants to stretch the word "religion" in this way, that doesn't settle the First Amendment question. For that purpose, the issue isn't what someone might decide to mean by the word "religion." It's what it means in the First Amendment. It's beyond doubtful that the Framers intended to count all moral considerations as religious, thereby ruling out broad moral considerations as legitimate grounds for legislation. What's pretty clear is that the Framers were concerned with religion more or less as we ordinarily think of it. And as we ordinarily think of religion, believing that murder is wrong isn't enough to make someone religious.
Your second major argument is an appeal to a kind of libertarian argument: while we're individually obliged to help people, we can't take people's money by threat of violence and use it for the benefit of others.
For that line to be persuasive, the analogy between government programs and holding someone up at gunpoint to get their money for Granny's good has to be a sound one. When you put it the way I just did, however, it seems a little less than convincing.
I'd be prepared to go further. I think that part of what the analogy rests on is a doubtful view about what's "yours" or "mine" in the first place. What you own you own against the background of a large and complicated social scheme. There's no straightforward fact of the matter about what "really" belongs to you and what doesn't. Your claim about how we should or shouldn't treat people and their money is a moral claim. There's nothing wrong with that; the questions here are in large part moral ones. But since you're appealing to a moral notion of property rights, you need a moral argument that's a lot more detailed and careful than the analogy with robbery (or Robin-Hoodery...)
There are deep, serious and important questions about the proper limits of government. There are serious arguments to be made that lean libertarian, and there are equally serious arguments that tend in quite the opposite direction. This comment—already too long—isn't the place to sort all this out. My plea really comes down to this simple thought: there really is a serious issue here, and engaging it will call for going beyond slogans and problematic analogies. There's too much at stake for that.