Environmental, social, and governance (ESG) factors are increasingly analysed to identify the risks and opportunities in contemporary economies. The banking sector influences the whole economy through the credit channel and balances its stability. The interplay of these elements motivated our main question, whether ESG scores impact European financial stability, measured for the banking sector. To this aim, we employ the cross-quantilogram methodology, which explores dependences at all levels of the distributions of two random variables. To determine the quantile dependence, we resort to methods of measuring systemic risk (Marginal Expected Shortfall—MES, CoVaR, and ΔCoVaR) for all commercial banks listed on European stock exchanges. While our approach provides a dashboard for analysis of the dependence of financial stability on ESG pillars, our findings indicate that such a connection is valid and cannot be identified with standard approaches that explore average distribution levels. We also document the differences in these impacts across the ESG pillars.