What sect of Traditional Catholicism is Mel Gibson and, by extension, his Holy Family chapel in Malibu, CA affiliated with? This article below connects it to the World Faith Foundation, the Aquarian Education Group, etc., but not anything as recognizable as the SSPX, SSPV, CMRI, etc. Excerpts:
St. Michael’s and its clerical leader, like the Holy Family Church in Malibu, are not recognized by the archdiocese. The new church is officially supported by something called the World Faith Foundation, which in turn is named in papers filed by another charity, James Hirsen’s Foundation for Free Expression, as an affiliated group.
Meanwhile, Holy Family’s religious leader is named on a Web site for independent Catholic churches in California as the Most Reverend Tourkom Saraydarian , who lists his own religious affiliation as the Aquarian Education Group. It’s not clear what if any association Saraydarian may have had with a religious philosopher of the same name who died in 1997.
I believe it can be said that Mel Gibson and his private chapel are not affiliated
with any particular sect. Many of those "70 members" that the article mentions (Gibson included) were former attendees of Our Lady of the Angels chapel in Arcadia, CA, which was pastored by a so-called
"independent" priest named Msgr. Donohue (+RIP).
More about Msgr. Donohue can be read here: http://www.sspx.org/Chapels_Pages/arcadia_ca.htm
The reason(s) for Gibson and others to not attend Mass in Arcadia after the SSPX took over the chapel are not known by me with any level of certainty. One could speculate "sedevacantist reasons" for their avoiding the SSPX. One could equally speculate hesitancy towards an order that had been accused of being schismatic. And... there could even be the explanation that they live a whole heck of a lot closer to Malibu than Arcadia.
I wish the article was a bit more specific (i.e., providing the source) for the "Most Reverend Tourkom Saraydarian" leadership of Holy Family...
To the best of my knowledge (from news reports), the World Faith Foundation has 2 churches: one in Malibu, CA and one somewhere in PA. Mel attends one, his father attends the other. I'd speculate it's how Gibson's accountant keeps his finances straight; i.e., separating his taxable income from the religious/charity/non-profit activites.