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Excerpt from article: Opus Dei
Wikipedia [link to en.wikipedia.org]

[...] In the English-speaking world, the most vocal critic of Opus Dei is an internet-based blogging website called the Opus Dei Awareness Network (ODAN). ODAN describes itself as an organisation that exists "to provide education, outreach and support to people who have been adversely affected by Opus Dei." ODAN is headed by Diane DiNicola, mother of a former member, Tammy DiNicola. Other major critics include Maria Carmen del Tapia, an ex-member who was a high-ranking officer of Opus Dei for many years, liberal Catholic theologians such as Fr. James Martin, a Jesuit writer and editor, and supporters of Liberation theology, such as journalist Penny Lernoux and Michael Walsh, a writer on religious matters and former Jesuit. [...]
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E​xcerpt from article: Their Will Be Done
Mother Jones magazine, 1983 [link to motherjones.com]

[...] Opus Dei powerbrokers have gained enormous influence inside the Vatican since they helped install the current pope. The courting of John Paul II began when he was still the archbishop of Krakow. He was asked to speak at Opus Dei colleges and at the group's international headquarters in Rome. In an effort to enhance Wojtyla's image as papabile, these speeches were printed by Opus Dei in book form and circulated among members of the Vatican hierarchy. When Karol Wojtyla became pope, he returned the favor by elevating Opus Dei to the unique status of a "personal prelature." Critics of Opus Dei fear that the pope's edict will allow its members to elude the authority of local bishops in special circumstances, thereby strengthening the order's tendency to function as a "church within a church." This was an important victory for Opus Dei, which had been rebuffed on previous occasions by both Pope John XXIII and Pope Paul VI.

The decision to upgrade the status of Opus Dei appears to be part of an over-all strategy to counter the influence of Jesuits and other progressive clerics active in the liberation theology movement.

Pope John Paul II's feud with the Jesuits came to a head in October 1981, when he suspended the order's constitution and replaced its ailing superior general, Father Pedro Arrupe, with a Jesuit of his own choosing. Many Jesuits have caused turmoil in the Vatican by questioning papal pronouncements on birth control, priestly celibacy, the barring of women from the priesthood and, most significantly, clerical involvement in politics. [...]
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Related
Thread: The Pope on Liberation Theology (Marxism) in his Church