Among the three religions of Confucianism, Buddhism, and Taoism, the inheritance mode of Confucian cultivators is somewhat different from that of Buddhism and Taoism. They mostly propagate their teachings through academies. After studying for a period of time, they will leave the mountain and integrate into the society, there usually isn't a consistently followed Sect.
After leaving the academy, each would go their own way. Besides some who remained in the academy to teach, others would seldom have any relation with the academy. If the bond was strong, they might just do something for the academy once they achieve success in the future. They have a high degree of freedom.
If the cultivators of Buddhism and Taoism left their sect gates and established their own sects, it didn't matter; but if they joined other sects, there would inevitably be a bit of a traitorous implication.
