NLP models are dependent on the data they are trained on, including how this data is annotated. NLP research increasingly examines the social biases of models, but often in the light of their training data and specific social biases that can be identified in the text itself. In this paper, we present an annotation experiment that is the first to examine the extent to which social bias is sensitive to how data is annotated. We do so by collecting annotations of arguments in the same documents following four different guidelines and from four different demographic annotator backgrounds. We show that annotations exhibit widely different levels of group disparity depending on which guidelines annotators follow. The differences are not explained by task complexity, but rather by characteristics of these demographic groups, as previously identified by sociological studies. We release a dataset that is small in the number of instances but large in the number of annotations with demographic information, and our results encourage an increased awareness of annotator bias.