Conversational robots powered by artificial intelligence (AI) are intensively implemented in the insurance industry. This paper aims to determine the current level of acceptance among consumers regarding the use of conversational robots for interacting with insurers and seeks to identify the factors that influence individuals’ behavioral intention to engage with chatbots. To explain behavioral intention, we tested a structural equation model based on the Unified Theory of Acceptance and Use of Technology (UTAUT) model. It was supposed that behavioral intention is influenced by performance expectancy, effort expectancy, social influence, and trust, and by the moderating effect of insurance literacy on performance expectancy and effort expectancy. The study reveals a significant overall rejection of robotic technology among respondents. The technology acceptance model tested demonstrates a strong ability to fit the data, explaining nearly 70% of the variance in behavioral intention. Social influence emerges as the most influential variable in explaining the intention to use conversational robots. Furthermore, effort expectancy and trust significantly impact behavioral intention in a positive manner. For chatbots to gain acceptance as a technology, it is crucial to enhance their usability, establish trust, and increase social acceptance among users.