•Applies intergroup conflict to unhoused users in public parks and greenspaces.•Equitable management requires an understanding of conflict.•Park users described both social values and interpersonal conflict.•Negative attitudes towards unhoused people was related to greater conflict.•We describe strategies to address conflict in this context. Like other user groups, people experiencing homelessness utilize parks and other public spaces for a variety of reasons, including recreation/leisure, physical activity, socializing, and to enjoy time in nature. However, unlike other user groups, unhoused park users also often rely on parks as a setting to engage in a variety of necessary metabolic and biophysical functions. Despite the centrality of these places to both unhoused and housed members of the public, there is little research focused on managing them for equitable outcomes between these two groups. We situate our work in this context, and specifically apply intergroup conflict as a framework for our analysis and discussion. Our results indicate that housed park users felt both interpersonal and social values conflict related to specific scenarios involving unhoused users. In general, those with more negative attitudes towards people experiencing homelessness were more likely to report conflict with unhoused park users. The greatest levels of conflict were perceived in the context of non-normative park use by unhoused users (activities that would be unacceptable by any user group). We suggest a variety of passive and active management strategies to reduce perceived conflict between unhoused and housed park users, including specific zoning, amenities, enforcement, and educational strategies.