The common ground between the Red Lantern Society and the Qianjin Church lies in their aim to seek welfare for women.
However, the point of disagreement is that the Red Lantern Society leans more towards a traditional family lifestyle of supporting a husband and educating children, while the Church encourages and supports women's independence and self-expression.
As to who is right and who is wrong, it's really hard to make a hasty conclusion.
From the personal standpoint of Wang Yunxiao, he didn't think there was anything wrong with the ideologies of these two organizations, both seemed like very normal aspirations.
But what others thought, or what the reality was, that was hard to say.
The Red Lantern Society was currently experiencing internal conflict, and the specific reasons were not known to outsiders. Since the Qianjin Church was also interested and had specifically sent people to cooperate with the police, Wang Yunxiao was more than happy to pass on the burden.