Polly, just as a thought, you might try acknowledging that the system is racism and classist, and that they have certainly suffered unfairly from that. Then, when you offer to help them, you can avoid seeming to define them as inadequate, and you're also not denying their experience and perceptions, but rather making it clear that you want to help change that system.
Perhaps I'm being defeatist, but my efforts in that area haven't worked very well with people who come to me from the start with the chip on their shoulder. I do very well with people who start out acknowledging that they came from crummy backgrounds and who need the pep talk to keep trying. I do ok with people who are just finding out how crummy their schools were and need the pep talk to keep trying.
I don't do very well with students who start with "I don't want to be here, but I am an A student and yet you gave me a 2 out of 3 on this quiz. Racist!", even during the parts of class where I am the cheeriest cheerleader that I can possibly be as I acknowledge that these parts are difficult for everyone, but let's give it a shot together. Those people were lost before they started.
I also don't do very well with the students who make practically no effort (as in missing 5 of the first 7 classes) and then scream that I'm a racist/classist/whatever for assuming that everyone can attend class ALL the time instead of just "most" of the time. Whatever else is going on, that part of my class and indeed most of college isn't going to change, even if that is some sort of -ist.