Historical Influence
In my opinion, I feel like despite the deities' gender in mythological stories, many important religious leaders are still male. This may contribute to the conception of women as "other". In one of the Chinese creation myth, the deity that created the world was a female, and she was considered the mother goddess. However looking at the historical settings of China, it was a very male dominant society in many aspects such as religion, economy and more. Therefore I think although religion does play an important role in how people view their surroundings, it does not influence the image of women that greatly.
I do not know to what extent religion has affected the "other-ing" of women in Japan as a whole but, I've heard that in Japanese religion like Shinto and Buddhism, women were seen as polluted things. They were considered unclean and thus were banned to enter sacred places like the shrine, mountains and ritual places. This still exists till today and it is why the monks that work at shrines are still male dominated. However, as a whole society, I believe that we do not see much gender equality formed through these religions as much as it does in Christianity/ Catholicism.