The population suffering from mental health disorders has kept increasing in recent years. With the advancements in large language models (LLMs) in diverse fields, LLM-based psychotherapy has also attracted increasingly more attention. However, the factors influencing users' attitudes to LLM-based psychotherapy have rarely been explored. As the first attempt, this paper investigated the influence of task and group disparities on user attitudes toward LLM-based psychotherapy tools. Utilizing the Technology Acceptance Model (TAM) and Automation Acceptance Model (AAM), based on an online survey, we collected and analyzed responses from 222 LLM-based psychotherapy users in mainland China. The results revealed that group disparity (i.e., mental health conditions) can influence users' attitudes toward LLM tools. Further, one of the typical task disparities, i.e., the privacy concern, was not found to have a significant effect on trust and usage intention. These findings can guide the design of future LLM-based psychotherapy services.