Climate-controlled cabins have for decades been standard in vehicles. Model Predictive Controllers (MPCs) have shown promising results in achieving temperature tracking in vehicle cabins and may improve upon model-free control performance. However, for the multi-zone climate control case, proper controller tuning is challenging, as externally, e.g., passenger-triggered changes in compressor setting and thus mass flow lead to degraded control performance. This paper presents a tuning method to automatically determine robust MPC parameters, as a function of the blower mass flow. Constrained contextual Bayesian optimization (BO) is used to derive policies minimizing a high-level cost function subject to constraints in a defined scenario. The proposed method leverages random disturbances and model-plant mismatch within the training episodes to generate controller parameters achieving robust disturbance rejection. The method contains a postprocessing step to achieve smooth policies that can be utilized in real-world applications. First, simulation results show that the mass flow-dependent policy outperforms a constant parametrization, while achieving the desired closed-loop behavior. Second, the robust tuning method greatly reduces worst-case overshoot and produces consistent closed-loop behavior under varying operating conditions.