When you push people to the edge of society by not allowing them a place within it, you marginalize them. If a public school celebrates only Christmas in December, it can marginalize students who aren't Christian.
A society that labels certain people as outside the norm — weird, scary, hateful, or useless — marginalizes those people, edging them out. Native or aboriginal groups often end up in this position, and so do people who are poor, disabled, elderly, or who in other ways are seen as not quite fitting in. The Latin root is margo, "edge, brink, or border." Since the late 1920's marginalize has referred not to a literal edge, but to a powerless position just outside society.