How does a shift in climate policy affect financial stability? We develop a quantitative macroeconomic model with carbon taxes and endogenous financial crises to study so-called "Climate Minsky Moments". By reducing asset returns, an accelerated transition to net zero initially elevates the crisis probability substantially. However, carbon taxes enhance long-run financial stability by diminishing the relative size of the financial sector. Quantitatively, the net financial stability effect is only negative for higher social discount rates. Even then, the welfare effects of "Climate Minsky Moments" are, at most, second-order relative to the real costs and benefits of an accelerated transition.