Financial markets are highly unpredictable and often associated with tail risks. This study examines the tail connectivity among three distinct markets—conventional, religious, and sustainable—and uses a new neural network quantile regression technique to quantify their risk exposure. The findings suggest that traditional and religious investments have the greatest tail risk exposure during crises, emphasising the importance of diversification using sustainable investments. The Systematic Network Risk Index identifies intense events, such as the COVID-19 pandemic, the European debt crisis, and the global financial crisis, as having the greatest tail risk. The Systematic Fragility Index finds the Islamic stocks during the COVID-19 crisis and the conventional stock market before the pandemic to the highly vulnerable markets. On the other hand, the Systemic Hazard Index identifies Islamic stocks as the primary source of systemic risk. The study concludes by providing implications for decision-makers, regulatory authorities, investors, players in the financial system, and investment managers to diversify their risk by utilising green/sustainable investments.