Issues as these are involved:
Culture is customs, beliefs, myths, sociology of knowledge, forms of language and expression, shared assumptions (core paradigms). Core of identity and communication is involved, so also are shared preferences and religion/ attitude to religion.
An initial question is how far is liturgy and its assumptions away from the root paradigms of thinking that takes place now. It is not a question that was once asked, but it is now as religion is inherited from a thoughtform world that seems to come from a museum.
If liturgy is distant or cut off from society in terms of thoughtforms and numbers participating, then presumably it plays little social role. A liturgy that involves a large proportion of inhabitants and involves how they think can play a binding role in society in terms of repeating and reinforcing those beliefs and values within the liturgy.
It may be best not to consider, any more, a wider social role for liturgy. All church attenders are minorities now, and it is a matter of choice whether the content connects with common thoughtforms or not.
There are different ways to connect with culture. One is that the form is culturally connected, even if the content is not: so much evangelical and charismatic worship is like this. It taps into the pop and rock music world and is highly entertaining, but the message is of that old time religion. The people who like the form, and also the fellowship, are faced with a choice to adopt the content or not - to become converted or lose out on the entertainment and fellowship.
In some cases, as in say the Unitarians, the content is more or less connected with basic social key paradigms but the form is inherited (as in a hymn sandwich preaching service).
In other cases form and content may be ancient, although in some cases the requirement to believe is relatively untested or broad, as in some Orthodoxy and also much Anglo-Catholicism. It is light-touch package deal participation. It's as if the priests know and preserve the tradition and the laity can simply follow it along.
Contextualisation assumes a body of theological knowledge, and so liturgy follows this but tries to do so in local circumstances, they being urban, or deprived, or suburban and middle class, or demanding education, or exploited, or landowning, or rural. Liturgy, like the Christian religion, should show a bias to the poor, but it also shows a bias to authority, class and political power.
Recent Roman Catholic liturgical changes, far from being the inculturation of Vatican II in 1963 have been high and authoritarian translations handed down, thus producing an unsatisfactory English form of ritual.
Oddly, Unitarian liturgy when 'given' was based, at root, on the Church of England Book of Common Prayer. Samuel Clarke produced an Arian version of this, to find its use in Theophilus Lindsey's first-named Unitarian church; and revisions of liturgies followed the Anglican model with the reference points and doxologies either the economic trinity only or an emphasis on the Father God. So much of this has given way to individualist services of the free form; few liturgies have been written and with an absence of liturgical principles. There are now a scatter of resources of fragments written by ministers and others.
Kings Chapel Boston (USA) is a liturgical museum regarding the active use of Arian/ Unitarian pre-set forms again with origins in Anglicanism. This is despie Anglicanism and Congregationalism being a sharper competitor in the United States. In the UK the parish Presbyterian identity was a culture of 'openness' to include the Anglican-style liturgy that was then recognisable (with all Popery stripped). The move to denominationalism was also a move to Free Church flexibilities.
Liturgy acquires an importance of identity in postliberal situations where a church ceases to relate to a worldly objective knowledge but the church still has to function like a church and use its own internal meaning. Thus its theology has to be expressed. The Unitarian right wing has often behaved like this: as if church services should have compulsory elements such as the Lord's Prayer and at least one Bible reading. Other churches, as they pluralise, just have these as optional.
Even within Christianity, liturgy can draw on and Christianise indigenous beliefs and forms, but the issue for Unitarians is not to vulgarise what it uses. For example, a liturgy that is heavily theist and then continues with the apparent Buddhist equivalent of the beatitudes is more than likely doing violence to the original Buddhist source. My view on this is to have choices of liturgies: to have one more humanist, one more Eastern, one more Christian and so on, or have them thematic like science and awe or environmental and care.
What is clear is that many of the liturgical resources of the past are no longer usable. Orders of Worship of 1932 still assume a causal God, or one that can be addressed and listens. The language is heavy and like a holiness bubble, somewhat disconnected. It is possible to rewrite the material, with a transcendence that comes, as it were, from below, from life itself, and inbuilt values rather than inbuilt theologies. The bizarre reality is that some Anglicans often can continue to use 1662 material in its absurdity of feudal thought-forms and its now absence of communication, but having perceived 'transcendent' quality, whereas something that was changed and evolved like Orders of Worship has become out of date.
A liturgy should reflect a church service being a material effort to come together in the pursuit of a hope of a spiritual gift. There should always be an exchange/ gift understanding involved. This is because exchange and gift is a binding process, as is religion. To be an exchange involves a process, so a service should achieve a moving through and moving on from its beginning to its end. In a sense it is a life-marker and a refreshment. The service content should engage with the self and with the world, inward and outward. It involves being sorry and being thankful, and should not be over-critical in being sorry in terms of damaging the self. The sense of thankfulness is more important than its direction anywhere: it can be dispersed thankfulness. This can be combined with an outlook, a subject area, and does not have to be associated with old thought-forms. The liturgy should also allow 'drifting away' as part of one's general reflection in the place; no one should ever be asked what they can remember of the service.
There are some theological issues to face, in the movement towards simplicity of language even folk belief (in the Unitarians, too). Some object to 'sorry' rather than a stronger, restorative, 'repentance', but repentance depends on a theory of sin which Unitarians have, classically, rejected. Unitarians have had an optimistic view of humankind, whereas Universalists have had a more pessimistic view but thought all would be saved (that's the old difference between those categories, that merged in the USA, but also confused by the Arminian debate and a chase towards universalism in general even within the Unitarians). So, indeed, saying sorry is sufficient and humanistic. But what of folk belief?
This arises in the joined question: what do Unitarians do about Easter and Christmas? They do not have the cult of the individual, although early Unitarians certainly believed in the biblical resurrection in their regard for Jesus as the supreme chosen prophet. Later Unitarians joined the resurrection debate, and later still dropped the arguments as of central concern. Nevertheless some return to these debates at Easter, whilst for others Easter is about rebirth in general and the strength of Spring. Christmas becomes another rebirth time, one more associated with hope than realisation (more surely a case of certainty than hope, however). Christmas is the most 'folk' belief time, so that the carols get sung without the theological justification behind them. Nearly everyone 'joins in' (some stay away) with this as some sort of universal baby festival. So it is a kind of Christian Hinduism, based on stories of an infant. It seems that questions of whether this is honest or consistent get dropped for the duration of the party. And whereas Anglicans and Catholics in particular hold on to Advent and celebrate Christmas on and after the breaking of 25th December, Unitarians have adopted the commercial Christmas so that, whilst Advent might get a nod, Christmas is in the few weeks up to and including the 25th, and the carols get dropped soon after as questions of honesty and consistency get restored. So there is a kind of residue of cultural Christianity at Christmas, but less so at Easter which is ever more Pagan.
Central to all this is the place of miracle and absence of belief in the extra-scientific. Mainstream Churches have had problems with reforming liturgy towards ordinary thought. Because they are wedded to subscribed beliefs, liturgical reform is little other than the modernisation of language. But the modernisation exposes the meaning form of the original and imposes thought forms not used outside the church. People know that crops grow because of their evolved capture of the energy of the sun turned into growth, and it is silly to pray for rain. Yet one can be thankful for water and for the process of energy consumption and food, for borrowing against the larger process of entropy for some transitional moments. So, again, it is about simpler expressions of being human.
Unitarians then should be free of content that has to include somehow a man that is begotten or made divine, or a causal, intervening God. Inbuilt can be naturalistic explanations, yet still drawing on ethical and religious traditions around the world.
The problem is that change, having caught up on belief, emphasises the transitional nature of communicative reality, and this works against anyone producing liturgies. But with principles in place (of process, exchange/ gift, and ethics) it should be possible to draw on local meaning and make liturgies that have some longevity. If well written they may involve the repetition that gives rise to a sense of sharing, bonding and over all transcendence.
Gover, David (1993), 'Liturgy and Culture: Is Modern Western Liturgical Revision a Case of Not Seeing the Wood for the Trees', in Bradshaw, P., Spinks, B. (eds.) (1993), Liturgy in Dialogue, London: SPCK, 28-49.
Pluralist - Liberal and Thoughtful