Although guidelines for human-AI interaction (HAI) are providing important advice on how to help improve user experiences with AI products, little is known about HAI for diverse users' experiences with such systems. Without understanding how diverse users' experiences with AI products differ, designers lack information they need to make AI products that serve users equitably. To investigate, we disaggregated data from 1,016 human participants according to five cognitive styles -- their attitudes toward risk, their motivations, their learning styles (by process vs. by tinkering), their information processing styles, and their computer self-efficacy. Our results revealed situations in which applying existing HAI guidelines helped these cognitively diverse participants equitably, where applying them helped participants inequitably, and where stubborn inequity problems persisted despite applying the guidelines.The results also revealed that these situations pervaded across 15 of the 16 experiments; and also that they arose for all five of the cognitive style spectra. Finally, the results revealed what the cognitive style disaggregation's impacts were by participants' demographics -- showing statistical clusterings not only by gender, but also clusterings for intersectional gender-age groups.