In Jin Yong's fictional wuxia universe, there's a certain irony that connects the Ming Cult of HSDS to the Heaven and Earth Society of HSDS.
In Jin Yong's world, the Ming Dynasty was the only Chinese imperial dynasty born *directly* out of a wulin organization. The Ming Dynasty was founded by Chu Yeun Cheung, who was a Ming Cult member during his wulin days. When Chu overthrew the Mongols and founded his new imperial dynasty, he gave it the name of the wulin organization of which he had once been a member.
Three hundred years later, the dynasty that Chu established and had given his cult's name was defeated and China was again ruled by a foreign dynasty - this time, the Qing Dynasty of the Manchurians. A new wulin rebel organization, the Heaven and Earth Society, was founded by the last Ming Dynasty loyalists to oppose the Qing rule.
There's a certain irony that the dynasty founded at least partially due to the activities of an anti-foreign government wulin group would be, after its demise, championed by yet another anti-foreign government wulin group. The Ming Dynasty's history in Jin Yong's world is bookended by the Ming Cult and the Heaven and Earth Society.