I think McIntosh's thesis in "White Privilege and ...." explains Carillo's perspective in "And When You Leave...". Part of McIntosh's explanation of the anger racial minorities feel towards white liberals, male and female, is that white people, liberals and conservatives, enjoy a privilege in this society for being white, but they do not realize that they are enjoying such privilege and this makes minorities resentful against whites, even on the occasions when white people are trying to be allies in the struggle for minorities' rights. "At the very least, obliviousness of one's privileged state can make a person or group irritating to be with." McCintosh, Peggy "White Privilege and Male Privilege..." . If people enjoying a privilege do not recognize that they do so, then they cannot work to end it. I think McIntosh's reading also ties with "The Bridge Poem", that until you really get to know yourself, including any privileges enjoyed, you cannot be a bridge. You have to realize whether or not enjoy privileges, in order to be able to work to make society function more on the basis of merit rather than on personal traits that have nothing to do with merit.
"And When You Leave..." also touches on class. The black and brown women in the poem are working class women, farmers and factory workers, while the "white sisters" background is not really described in the poem, but it is pointed out in several parts of it that the white sisters "own pictures", which give a sense of economic power, to be able to "purchase" an image in order to give the message that you care. I believe the poem clearly depicts the big schism between the poor and the upper middle class, which is more significant than the fact that the poor brown and black women are "sisters" with white women. I believe that this poem's theory is that in the hierarchy of societal factors to unite or separate groups, class is more significant than gender too.