Is Independent Catholicism even Catholic?
Yes, definitely. There are several expressions of Catholicism, and many churches comprise the "one, holy, catholic and apostolic Church" professed by all.
The Roman Catholic Church is the world's largest and most well-known expression of Catholicism. In Asia and Eastern Europe, however, the most prominent face of Catholicism is the Orthodox Catholic Church, which possesses over 300 million adherents and which excommunicated the Roman Catholic Church in 1054 A.D. for its deviance from the ancient creed of the Church, its insistence on unleavened bread, and its imposition of the novelty of clerical celibacy.
What do all Catholic churches have in common?
All Catholic and most Christian churches profess faith in the "one, holy, catholic and apostolic Church."
Relating with one another as sister churches, these members of the universal Church believe that by baptism, we become members of the one Body of Christ and are nourished by the eucharist. The apostolic faith handed down to us also teaches that there are other sacraments we celebrate during crucial moments in life.
Like sisters in the same family, these churches share various similarities but differ. As sister churches, most of our differences are administrative and disciplinary, but some are ecclesiological and theological. Differences are to be expected; not all sisters are the same.
Still, we are united by those bonds that we all hold dear: baptism, eucharist, and apostolic
How can Independent Catholic churches claim to be apostolic churches?
The litmus test of any Catholic church is apostolic succession. Most Independent Catholic bishops are validly consecrated by other bishops possessing valid lines of series from the apostles, including the lines of apostolic succession from the Roman Catholic Church, the Old Catholic Church, the Malankara/Syrian/Jacobite Churches, and various Orthodox Churches.