Is a wife obligated to obey her husband if he asks for the access credentials to her social media accounts, in exchange for giving her his own accounts, knowing that the wife's accounts are private to women and may contain their photos?

You are not obligated to obey your husband by giving him the login password to your social media accounts, especially if they contain pictures of your female friends. It is not permissible for you to enable him to access them. Nor should the husband request that. However, if he requests it and enabling him would not lead to a religious transgression or harm, then it is preferable not to prevent him, in order to gladden his heart and reassure him. The foundation of the relationship between spouses is trust and compassion.