Ping
Pope John Paul I met personally with Kiko and Carmen when he was still Patriarch of Venice in 1972, permitting them to open a community in his diocese, and encouraging the movement's progress in the following years.
Pope John Paul II has always supported the movement, even in his days as cardinal of Cracow. He visited the Neocatechumenate community of Porto San Giorio on December 30, 1988, where, for the first time in our days, a Pope celebrated, the Pope praised the movement's "fruits" of personal conversions and missionary inspiration. In 1990, the Neocatechumenates received their first official papal recognition, in the letter to Bishop Cordes mentioned above.
Years later, on May 9, 1986, Kiko and Carmen were summoned by the Congregation for the Doctrine of the Faith to respond to a series of questions regarding their views on hermeneutics, pastoral work and doctrine. After thorough study of their responses, Cardinal Joseph Ratzinger informed them that his Congregation wished to assist them, and proposed linking the movement to a Vatican congregation to provide a juridical basis. Kiko and Carmen fervently desired the official support of the Holy Father. As a result, John Paul II nominated Bishop Paul Josef Cordes, Vice-President of the Pontifical Council for the Laity, to act as the Pope's delegate ad personam to the movement and intermediary with the Vatican Congregations.
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It sounds to me like the Magisterium's view of the facts is different than that of the sspx. I trust the Magisterium.