The rapid development of generative artificial intelligence (AI) and large language models (LLMs), and the availability of services that make them accessible, have led the general public to begin incorporating them into everyday life. The extended reality (XR) community has also sought to integrate LLMs, particularly in the form of conversational agents, to enhance user experience and task efficiency. When interacting with such conversational agents, users may easily disclose sensitive information due to the naturalistic flow of the conversations, and combining such conversational data with fine-grained sensor data may lead to novel privacy issues. To address these issues, a user-centric understanding of technology acceptance and concerns is essential. Therefore, to this end, we conducted a large-scale crowdsourcing study with 1036 participants, examining user decision-making processes regarding LLM-powered conversational agents in XR, across factors of XR setting type, speech interaction type, and data processing location. We found that while users generally accept these technologies, they express concerns related to security, privacy, social implications, and trust. Our results suggest that familiarity plays a crucial role, as daily generative AI use is associated with greater acceptance. In contrast, previous ownership of XR devices is linked to less acceptance, possibly due to existing familiarity with the settings. We also found that men report higher acceptance with fewer concerns than women. Regarding data type sensitivity, location data elicited the most significant concern, while body temperature and virtual object states were considered least sensitive. Overall, our study highlights the importance of practitioners effectively communicating their measures to users, who may remain distrustful. We conclude with implications and recommendations for LLM-powered XR.