First, we should note that the Reverend Edwin Abbott, as were most schoolmasters and university tutors of the period, was an ordained priest in the Church of England. Thus in some ways, Flatland serves as an allegory of a secular world encountering the divine (e.g. when characters in the Bible encounter the risen Jesus). Just as Flatlanders can only perceive in two dimensions and must use reason and intuition to extrapolate the nature of multidimensional objects, our knowledge is also limited by what we can perceive in a world that might seem as limited to other beings as Flatland does to us. This sort of reading would emphasize the parallels between Abbott's work and the Allegory of the Cave in Plato's Republic; as Abbott was a Senior Classics medallist at Cambridge, he would have been deeply familiar with Plato.
Another possible parallel you could draw would be between the hierarchy of shapes in Flatland and the hierarchy of skin color in the United States, especially in the first half of the twentieth century. Just as it appears to us absurd that the beings of Flatland were judged by shape rather than character, morals, or intelligence, to many of us now it seems equally absurd that people were once judged by skin color, and that, for instance, where one could sit on public transit was once determined by the shade of one's skin.