Catholicism 101: To be Catholic one must be in communion with the church as a community of faith, that is both historically discernible, and present (living) sacramental and institutional reality. This community was established by Christ himself who has preserved it in truth and who instituted an authoritative hierarchy. 

Those who advocate for leaving the "...old ecclesial frames and opt for listening to the stories of one another's lives",  are no longer in communion with the Church and therefore are no longer Catholic.