We examine diverging preferences in human-labeled preference datasets. We develop a taxonomy of disagreement sources spanning 10 categories across four high-level classes -- task underspecification, response style, refusals, and annotation errors. We find that the majority of disagreements are in opposition with standard reward modeling approaches, which are designed with the assumption that annotator disagreement is noise. We then explore how these findings impact two areas of LLM development: reward modeling and evaluation. In our experiments, we demonstrate how standard reward modeling methods, like the Bradley-Terry model, fail to differentiate whether a given preference judgment is the result of unanimous agreement among annotators or the majority opinion among diverging user preferences. We also find that these tendencies are also echoed by popular LLM-as-Judge evaluation methods, which consistently identify a winning response in cases of diverging preferences. These findings highlight remaining challenges in LLM evaluations, which are greatly influenced by divisive features like response style, and in developing pluralistically aligned LLMs. To address these issues, we develop methods for identifying diverging preferences to mitigate their influence on evaluation and training.