In this paper, we conduct the first study on spurious correlations for open-domain response generation models based on a corpus CGDialog curated by ourselves. The current models indeed suffer from spurious correlations and have a tendency to generate irrelevant and generic responses. Inspired by causal discovery algorithms, we propose a novel model-agnostic method for training and inference using a conditional independence classifier. The classifier is trained by a constrained self-training method, coined ConSTrain, to overcome data sparsity. The experimental results based on both human and automatic evaluation show that our method significantly outperforms the competitive baselines in terms of relevance, informativeness, and fluency.