I wouldn't say so, ever. You and I (we?) certainly have the right to help them, but an obligation is an absolute, and the logical conclusion of obligation of this sort is Comte's altruism (i.e. self-immolation).
As for competition... I view it as a pleasant byproduct of, rather than the purpose for, Capitalist economics. Competition is neither a premise nor a conclusion, simply an observable phenomenon that happens to benefit just about everyone. The primaries in arguments for Capitalism are the ethics of rational self-interest; the freedom from such obligation is fundamental to a free market. Thus, policies designed to protect competition are anti-ideological, they're designed as means to a desired end. (I realize that's probably a bit tangential.)
I have no problem with that. I'm sure you're right in saying it's largely irrelevant, I intended only to allude to the infinitely-long list of questions neglected when a dilemma is posed along the lines of, "we have to take care of these people, or they'll die" (or whatever). Not that I'm accusing you of proposing such a dilemma.
What, specifically, do you find to be relevant to the discussion? I should like to weigh your premises, if you'll share them. (That's assuming you've reached a conclusion on this matter, which may not be a safe assumption.)
I don't know either. I'm not entirely sure that racially-motivated violence has really decreased at all, I suppose it would depend into what proportion we squeeze the figures. (I'm thinking Jena Six here.) It's also worth mentioning, I suppose, that racial violence may not be the best metric for grading intolerance. It's certainly true that actions are of primary concern, but a quick trip to the Main (or worse, 4chan) leads one quickly to the conclusion that racism is by no means dead. The internet is an interesting phenomenon. The anonymity is emboldening. Now I wonder what the consequences are in there being a venue for those who feel hatred to let their flag fly freely. Digression again, maybe.