While Independent Catholics do tend to fall into clusters based on theological identity — traditionalists, liberals, theosophically-inclined Catholics, Gnostic Catholics, etc. — they are wildly diverse when it comes to liturgy. Although some jurisdictions require the use of specific rites for the Mass, many give their priests substantial freedom to choose texts and rituals to fit their community; in a given jurisdiction, every community might use a completely different liturgy.
Below are links to liturgical resources I’ve found among Independent Catholic communities, as well as canonical resources that have in part inspired them. They give a taste of what can be experienced in the worship services of various churches.
Anglican Book of Common Prayer
Ascension Mass (from a parish of the Catholic Apostolic Church of Antioch)
Divine Liturgy of St John Chrysostom
Johannite Gnostic Mass
Liturgies of the Liberal Catholic Church International (LCCI)
Old Catholic Church of America Mass
Roman Catholic Mass (Novus Ordo)
Roman Catholic Mass (Tridentine)
The Wadle Mass (American Catholic Church, absorbed into the Catholic Apostolic Church of Antioch)
