When you can worship as unselfconsciously in a high mass, incense wafting, Anglo Catholic choreographed altar routine and equally in a down town black Pentecostal Holy Roller vaudeville show and not run a mile, be phased out or burst like an inflexible wineskin, then you will have come close to a truly Apostolic Age, Spiritually mature, experience of living in the Christian faith. The churches Paul planted were astonishingly different in character, but nonetheless churches. The New Testament bears witness to the fact that none of them had got all their theological ducks in a straight line, otherwise Paul would have had no occasion to write to them, explaining theological questions for them and correcting their mistakes and we would have had virtually no New Testament upon which to base an acceptable Christian praxis. .
There are different ways to grow in understanding. To put it somewhat philosophically, a (new) thing can become part of your mind without becoming part of your will. Merely being exposed to something you may have some misgivings about doesn't mean, and need not mean, that you will automatically start practicing it yourself. Being a committed Trinitarian, I would not recommend worshiping at a Unitarian Universalist congregation (to cite your example), but there can be no harm in learning about it (or perhaps even observing such a service for educational purposes). Having faith is the basis of the freedom to grow, faith in the promise that As for the rest: By definition, yes, if something is novel or modern, then it cannot be "traditional". Let us reflect for a moment once more on the passage quoted above. To take one well known example, the Creed's "...of one substance with the Father..." was most certainly not a traditional formulation of the Faith when it was adopted by imperial decree in 325 at the First Council of Nicaea. Many conservative churchmen at the time opposed it and spent the next several decades arguing against it, not because they were sympathetic to Arianism (indeed, many were not), but because the phrase was neither "biblical" nor "traditional". The Church ultimately accepted it because what the formulation says is true. Plenty of similar examples from throughout Church history can also be cited. Anyone familiar with both the Creed and the New Testament today should be able to recognize that what the Creed says accords with the plain sense of the Scriptures, but this was by no means obvious to the Church at the time. The implications of the Scriptures' plain sense, and the varying proposed summaries of it in the local baptismal creeds, had to be worked out before a certain harmony within the Scriptures themselves, and between the Scriptures and the Creeds, could be recognized in the fulness of their meaning. In other words, the plain sense can often have implications that are unanticipated, novel, and definitely untraditional, without thereby being untrue. The truth is what ultimately matters and what should be sought. As Hegel once so eloquently put it in the Preface to his Phenomenology of Spirit: