this is a subject near and dear to my heart, as i grew up in a very chaotic and impoverished family. i am one of the ones who "made it out" so to speak, and i find that whenever i talk about justice, poverty, hunger, welfare, etc., i get a lot of comments like "well you were able to make it out, why should we help these other people when there's someone like you who can do it on their own?"
first off, i tell these folks, no one does it on their own. i didnt have a lot of money, but my dad loved me, my grandma loved me, and my teachers believed in me and instilled a HUGE amount of confidence in me from a very young age. that confidence right there? in my opinion, it's the reason i'm fairly successful now.
secondly -- well this one is a little trickier. bear with me while i sort it out.
when you think about society from a societal level, you have to agree that, yes, racism, classism, poverty, and disenfranchisment exist. poor people get screwed with to an enormous degree -- no car? that means youre riding the bus 3 hours a day to your shitty job in the suburbs. no bank account? then hand over 3% of your check if you want the cash buddy. no grocery store in your neighborhood? then you are either riding the bus even more, or buying $3 wonder bread from the bodega.
a worldview which does not acknowledge these basic inequities does not honor the truth as most poor people live it every day. these inequities are something we as a society need to do our best to understand and address.
BUT ... and this is the magic but

... we dont live our lives from a societal point of view. when you are looking at your own life, being oppressed cant be the end of the story. yes, i was born with some inherent disadvantages like not having a stable home, but i refused to let that be the end-all of my life. i turned the societal-level truths into obstacles that i was determined to overcome.
in my opinion, that is the only way to reach poor people. acknowledge that they are screwed because they are. but let them know that's not the end of the story -- it's just the beginning. it's like the set up of "the fellowship of the ring" -- frodo is screwed for sure. but with time, effort, and determination, he is able to overcome the odds and make his contribution to the world. he didnt look at the odds and shrug and give up.
people also have to be exposed to examples of folks who have climbed out of the same bad situation into a more comfortable and better one. just as i am not instantaneously going to start speaking fluent swahili (a language i have never heard), someone who has never seen real live "success" is not all of a sudden going to start believing in it.