Thanks for the question.
The Antioch movement is a group of non-denominational Christians, who have focused on some of the fundamental aspects of Christian life, with a relationship with Jesus being the centerpiece. Fellowship and witness also hold importance. All these things are good, but as with most Protestant churches and organizations they lack adherence to the full Gospel of Jesus Christ, the Sacramental life, the Magisterium of the Church and so much more. When you look under the covers some heresy will be present.
While the Catholic Church has been so battered and in decline in recent decades it is no wonder that many other Protestant groups capitalize on the Catholic shortcomings. The attraction of young, enthusiastic like-minded Christians draws people into its ranks. There is plenty of positive energy, support and encouragement. If you are Catholic however, you will find that these things, while good, can only go so far, and when certain dogmatic differences come up, the false sense of unity becomes more apparent. True Catholic spirituality, devotion to the Blessed Mother, the Sacred Heart of Jesus (and all the very Catholic notions that it implies) are looked at with a "concerned" perplexity or discouragement. They will strip away all that is truly Catholic: no Eucharist, Confession, no Holy Orders, no penance or reparations for offenses committed against the Sacred Heart of Jesus or the Immaculate Heart of Mary, and many other devotions that mark our rich heritage that have not only been bequeathed to us from the Traditional teaching of the Church, but the lives of the Saints and the numerous appearances of Our Lady in so many places.
If I were to associate with such a group (and I would ultimately discourage it) I would only do so with the intent on evangelizing them to the fullness of the Catholic faith. Somebody is going to evangelize the other to their way of thinking, and I would only be interested in bringing people to the Truth of Christ's Church, the One Holy Catholic and Apostolic Church—the Catholic Church.