Even in the traditions that have codified beliefs that their adherents are supposed to subscribe to, individual interpretations of their creeds can and do vary wildly. Many Liberal Jews are atheists. Also, Jews (Orthodox and Liberal & Reform) say that there are many different interpretations of the Torah - they really enjoy debating them in the schul / yeshiva attached to the synagogue. In Christianity, there are 17 different models of the Atonement, and in practice, individual believers do not all believe the same things, even if they pay lip service to the idea that they should do. Even though Islam has a fixed set of beliefs, there's still room for interpretation of the Qu'ran. Surprisingly, the word fatwa means an interpretation or an opinion. So if you are unsure about what to do about a particular thing, you go and ask a mullah or a qadi for an interpretation of the Koran. So it is not assumed by most Muslims (except Wahhabis) that there is only one possible interpretation of the Qu'ran. (Personally I'd just do as I saw fit.) Even in evangelical Christianity, there are a variety of opinions about being gay (there was a study of this by Kirsten Aune, a sociologist).
There is religion as it's officially supposed to be according to the doctrine of the tradition in question; and then there's the reassuringly messy, fuzzy and human way that people actually do it. The problem is that no-one apart from liberal religionists will actually admit that the fuzzy messy human way of doing it is actually the best way.
In liberal religion, where the "divine" is usually viewed as immanent in the world, or as so diffuse that it's not a person, the source of authority is viewed as the self (as in one's conscience) and not a "higher power". Fundamentalists and orthodox types believe that God is the source of moral commandments. I do not believe this. There's an excellent book by Richard Holloway called Godless Morality which explains exactly why God being the source of moral commandments can't possibly work even if you actually believe in God (which he doesn't). The reason is this: because we cannot be sure what "God" wants, or even if s/he exists, we cannot claim in our moral pronouncements to speak for God. If two people both claim to be doing what God wants, but do exactly the opposite, how do we decide between them? By using ordinary evidence, reason and compassion to decide.
Many Unitarians prefer to emphasise shared values as the basis of religion, rather than shared beliefs. I think this is an important feature of Unitarianism, and is what holds it together despite the diversity of beliefs within it. It is there from the earliest beginnings of Unitarianism, in Francis David’s famous saying “We need not think alike to love alike”, and the tolerance of different beliefs is the basis from which our core values of freedom, reason and tolerance gradually emerged.
For myself, I see liberal religion as spirituality practised in community. Spirituality is another concept that is difficult to define, but I regard it as a sense of mystical connection with the universe and all beings within it. In feeling this sense of connection, we experience compassion for the sufferings of other beings, and empathy with their joys. We can enhance this sense of connection by finding a community with whom we can practice compassion and mindfulness; if we don’t engage in spirituality in a community setting, it can become self-centred and shallow, disconnected from everyday reality. We need the experience of actually living and sharing with others to enable us to grow and become our authentic selves. This can be done by the creation of a community of shared values, which models in microcosm the desired qualities of human community. Of course there will be conflicts and tensions, but it is in how these are resolved that the real values of the community will be tested and refined. It is only by this kind of radical openness and humility that the beloved community can become strong and genuinely inclusive.
I believe that the religious life is a shared spiritual journey towards greater communion with the cosmos, where Spirit descends into matter rather than escaping from it – but this communion does not involve the effacement of individuality; rather it is the celebration of diversity and the quest for authenticity, because the "divine" (the vision of ultimate worth) is the potentiality of all life to share in mystical communion. But we must expand our compassion to all beings, not just to those whose values we share, and we do this by engaging in social action – caring for the poor and the oppressed, protecting the environment, standing up for human rights, and promoting freedom, peace and justice.
Fundamentalist religion is often the cause of compassion being withdrawn from people whose beliefs are not shared. My ethics trump religion every time. I left Christianity when I was 15 or 16 because huge swathes of it conflicted with my ethics (it was homophobic, sexist, anti-life and believed that the only way to salvation was through Jesus' death on the cross — there are huge ethical problems with all of that). I left Paganism when I realised that it was in conflict with my ethics. I would do the same with Unitarianism if it was in conflict with my ethics. I am sure that not everyone feels this way, but I know a lot of other people who do.
Indeed, we cannot really expect others to be convinced that we are "mystical" or "spiritual" unless we put compassion into practice by helping others. The two aspects of religion go hand-in-hand: without a sense of connection there is no basis for compassion, and without the expression of compassion in the form of caring, the life of a mystic can be barren and unproductive.
Note: By "mystical" and "spiritual", I do not mean anything supernatural - I mean a passionate, poetical sense of communion with all that is. I know that atheists are capable of mysticism - e.g. Richard Dawkins describes a mystical experience he had in the introduction to The God Delusion.