Social event detection refers to extracting relevant message clusters from social media data streams to represent specific events in the real world. Social event detection is important in numerous areas, such as opinion analysis, social safety, and decision-making. Most current methods are supervised and require access to large amounts of data. These methods need prior knowledge of the events and carry a high risk of leaking sensitive information in the messages, making them less applicable in open-world settings. Therefore, conducting unsupervised detection while fully utilizing the rich information in the messages and protecting data privacy remains a significant challenge. To this end, we propose a novel social event detection framework, ADP-SEMEvent, an unsupervised social event detection method that prioritizes privacy. Specifically, ADP-SEMEvent is divided into two stages, i.e., the construction stage of the private message graph and the clustering stage of the private message graph. In the first stage, an adaptive differential privacy approach is used to construct a private message graph. In this process, our method can adaptively apply differential privacy based on the events occurring each day in an open environment to maximize the use of the privacy budget. In the second stage, to address the reduction in data utility caused by noise, a novel 2-dimensional structural entropy minimization algorithm based on optimal subgraphs is used to detect events in the message graph. The highlight of this process is unsupervised and does not compromise differential privacy. Extensive experiments on two public datasets demonstrate that ADP-SEMEvent can achieve detection performance comparable to state-of-the-art methods while maintaining reasonable privacy budget parameters.