The two books that have been the most help in bringing me up to speed on the ISM have been The Many Paths of the Independent Sacramental Movement, and The Other Catholics: Remaking America's Largest Religion. What I found in these and with some other reading and poking around online has revealed a world I didn't know existed. This is a hodge-podge of bishops and priests who claim (for the most part) apostolic succession without any binding ties to a larger communion. They mostly trace their lineages back either to bishops who parted with Roman Catholicism, or to some form of Orthodoxy. Various liturgies are used, from Roman Catholicism, Orthodoxy, Anglicanism, or elsewhere, and often these are homebrewed to some extent to fit the perspective of the priest or bishop running the show. Theologically they ranges from New Age/occult all the way over to extreme traditionalist, although what counts as 'traditional' depends on the tradition. That is to say, some on this end of the spectrum devoutly hold to the old Latin Tridentine Mass, others to the 1928 Book of Common Prayer forms, and so on. As for the New Age/occult side, that can get pretty weird, with Theosophy as a primary although not sole historic stream of influence.
What Protestants would identify as denominations the people of the ISM tend to think of more as 'jurisdictions.' Usually a bishop will provide holy orders (ordination) to priests with the intention that the bishop is at least symbolically 'in charge.' The system of bishops, priests/presbyters, and deacons that they employ dates back at least to the 2nd century CE, when many early Christian churches were using this model. It caught on and became the standard for orthodox Christianity until the Protestant Reformation. In western Catholic thought, influenced by Augustine of Hippo, the sacraments leave a mark on the soul, and this includes holy orders. Just as I will technically always be a Catholic in the eyes of the Roman Catholic Church, even through I left when I was 17 and am now a Unitarian Universalist, so every deacon, priest, and bishop will forever have their holy orders. In Roman Catholicism it's understood that clergy who are 'defrocked' or excommunicated are to cease using their priestly powers except in certain extreme circumstances. The ISM disagrees with that assessment.
If we're looking for commonality among the jurisdictions of the ISM, one could say that what ties them together is saints, sacraments, and succession. All seem to agree to some extent on the relevance of saints, often naming their parishes (when they have them) after one or the other of the saints. The sacraments are absolutely central to the life of the ISM. The eucharist in particular is emphasized, with some bishops and priests even holding private, solo mass in their homes as a form of private devotion. This is controversial even in the ISM. The reality is that ISM clergy often don't have a parish at all, and instead serve the general public as officiants for baptisms, weddings, and funerals. Divorced Catholics in particular can often find an independent Catholic clergy person to officiate for their new marriage, even providing a nuptial mass, and without it having to be held in a church building. Roman Catholic priests won't officiate elsewhere, such as beach weddings.
It's apostolic succession where ISM clergy focus their greatest attention. In order to bolster their legitimacy, bishops of the ISM have long 'collected' lineages, such that the various lines have permeated pretty much the entire movement. Since the legitimacy of holy orders is understood to be the correct intent and form, it happens that more conservative people have received their ordination/consecration from more liberal bishops.
The two primary issues I see with their understanding of apostolic succession are that it defeats the apparent original purpose of the practice, and it depends on an interpretation unique to western Christianity.
First, there was not one church from the very beginning. In the first centuries of the Common Era there were multiple Christianities. For a long time there was a misconception that it was 'the church' and 'the gnostics,' but in recent decades we've come to understand that much of what's been grouped in with gnosticism was, in fact, other varieties of ancient Christianity. In the thick of that multiplicity, emphasis was placed by some Christians on following leaders who had known the apostles personally, with the idea being that they were more likely to be 'right.' Then it became about who was associated with people who knew the apostles. And so it went in the 2nd century that bishops began claiming apostolic authority by association.
Second, the idea that apostolic succession can exist apart right doctrine and right worship (orthodoxy) relies on a very narrow interpretation of a western Christian idea that is not generally shared by the Orthodox, Copts, and others of ancient communions.
Most ISM clergy are unpaid volunteers, except when hired as officiants, and don't have as much availability as full-time clergy to extend pastoral care. They also usually lack the formal training required of mainstream clergy. On the point of education, it has to be acknowledged that many evangelical preachers also don't have that much formal preparation, but even in evangelicalism it's common for ministers to at least try to get an undergraduate degree in Bible. One of the defenses offered in my reading for independent clergy not obtaining earned, accredited degrees is that they don't have the resources to up and move to go to seminary. That objection is a bit dated, as now the Association of Theological Schools, the accrediting body for graduate theological education in the United States, allows for full-online MDiv studies. In fact, I'm currently studying for my MDiv in this model. Sure, there isn't a guaranteed paycheck in the end for ISM clergy, as there would be for priests in some churches, but if this is truly their 'calling' then why can't they make it work?
Going into my reading about the Independent Sacramental Movement I was open-minded. While I wasn't going to change my mind and run to join them, I figured that they had something to offer. I still think that they do, particularly in terms of extending ceremonial services to people excluded by the mainstream Catholic and Orthodox bodies. There are certainly some bishops out there doing good, as I've said, and some jurisdictions seem to be striving to do better. One that I've taken an interest in especially is the American National Catholic Church, based out of New Jersey. With several parishes in the United States, they seem like a very Vatican II type of body, with the same liturgy I grew up with (born in the 70s), and inclusive of women and ltbtq+ folks. Still, I haven't seen evidence of a strong family ministry, or really a lot other than their mass schedule. In the video at the bottom of this post is a recent news report about one ANCC parish providing gas cards to people for free, so that's nice.
By and large the impression I get of the ISM is that most of those involved are LARPing as Catholic or Orthodox clergy. Certainly that's not the case in every instance, but when a religious movement has more clergy than adherents, what else am I supposed to think?