Climate transition risks pose growing financial stability concerns, but research on quantifying climate policy impacts remains underexplored. This paper helps address this gap by evaluating how carbon tax (CT) and green supporting factor (GSF) influence China’s financial stability. An innovative dynamic stochastic general equilibrium (DSGE) model incorporating the banking sector is developed to quantify transmission channels, improving on conceptual studies. It reveals that more intense climate policies heighten impacts on financial stability, with CT improving it but GSF hampering it in the long run. However, both policies negatively affect stability initially, albeit insignificantly. These diagnostics underscore calibrating policy intensities and sequencing to balance climate and economic objectives. Furthermore, this study reveals asymmetric effects on polluting and non-polluting enterprises, with the former seeing reduced output and lending but the latter gaining. The differentiated approach proposed, tailored to firm emissions levels, provides key insights for unlocking smooth green transitions while maintaining financial system resilience. The paper makes important contributions by bringing together climate policies, adaptation, and financial stability. The findings offer insights into achieving a smooth climate transition while maintaining financial stability. Specific implications include starting with low CT on the heaviest emitters, gradually lowering risk weights for green lending, and using public incentives and investment to aid polluting firms’ transition. This study offers valuable quantitative insights for developing country-specific climate financial risk policies.