What Horwitz says is simply that he is struck by the commonality between these views. This might seem surprising to us because of how different these people are. Irma Jackson is seen at a ceremony in which people are remembering the efforts of the civil rights activists of the 1960s. Even so, Horwitz feels that her attitudes are very similar to those of many white Southerners as they think about the Civil War.
In both cases, there is a feeling that they were fighting the good fight even at the expense of major hardships. In both cases, there is the feeling that they tried their best against these hardships but did not really prevail. In this sense, Horwitz is saying that black Southerners and white Southerners have something in common. Both, he says, feel that they have a "lost cause" for which they fought in vain.