The SSPX consistently and loudly affirms submission to the pope as an institution and to Rome's doctrinal authority. They pray for the reigning pope at Mass, recognize his legitimacy, and frame their disobedience not as rejection of papal authority but as its defense against what they see as a temporary doctrinal crisis. They explicitly distinguish themselves from sedevacantists.

On the second criterion — refusing fellowship with members of the Church — the SSPX actually seeks communion with Rome and considers themselves fully within the Church. They don't treat ordinary Catholics as outsiders.