Conversational recommender systems (CRSs) provide personalised recommendations by strategically querying attributes matching users' preferences. However, this process suffers from confounding effects of time and user attributes, as users' preferences naturally evolve over time and differ among similar users due to their unique attributes. These confounding effects distort user behaviors' causal drivers, challenging CRSs in learning users' true preferences and generalizable patterns. Recently, causal inference provides principled tools to clarify cause-effect relations in data, offering a promising way to address such confounding effects. In this context, we introduce Causal Conversational Recommender (CCR), which applies causal inference to model the causality between user behaviors and time/user attribute, enabling deeper understanding of user behaviors' causal drivers. First, CCR employs stratification and matching to ensure attribute asked per round is independent from time and user attributes, mitigating their confounding effects. Following that, we apply the Average Treatment Effect (ATE) to quantify the unbiased causal impact of each unasked attribute on user preferences, identifying the attribute with the highest ATE per round as the causal-based attribute, i.e., causal driver of user behaviour. Finally, CCR iteratively refines user preferences through feedback on causal-based attributes. Extensive experiments verified CCR's robustness and personalization.