Today's service at Hull was presented by a once member now located well west of Hull and on the subject of Protestantism. The quip was made that over in Ireland the Dublin church was able to expand its numbers so well because a Catholic country allowed more free thinking. I think the answer is simpler: it has a residual attending church culture at a time of modernisation, so a Unitarian church might well touch both that change and yet draw on a still greater propensity to attend. But no doubt the more 'magical' views of causality of its recent now minister suited Ireland quite well. Plus it matters that Dublin was and is Unitarian rather than the Non-Subscribing Presbyterianism of the rest of the island of Ireland, where only a Belfast church and only now seems to be advancing its message and reach (towards gay tolerance in a rather intolerant region).
I like the services as today's, with a confident and informal and skilled conversational presentation. My own tend to be more 'newsreader' like in style. He raises interesting questions but some times and including today I get the sense they go unanswered. So as well as the question of whether Unitarians are Protestant and proud of it, we had music from the Protestant break out period (I also threw in some English madrigals, a reference to Anne Boleyn and Protestant-affected music).We had a bit about Luther, but not the point that Luther was the most Catholic of Protestants, as is the Church (think of consubstantiation, for example). As for the Bible being supreme, but a Catholic pointing out that the Church chose the Bible, there was again nothing on higher Church Protestants: some Protestants do have a strong view of Church (and I'm not talking about Anglo-Catholics). We seemed to jump, for a Unitarian stance, from that straight to Martineau and individual authority. But that is post-biblical, even post-Church. There was nothing on the Bible and 'ordinary comprehension' as practised by the Reformation Socinians and Unitarians too. In other words, although yes the Bible was chosen by the Church, the Bible is then subject to individual reading and making sense of what is on the page (this is prior to biblical criticism).
The answer to the Church chose the Bible conundrum is that of Revelation. The Church is faithful to revelation (via the Holy Spirit) to the proper reception of the Bible. The Church rightly creates Articles and Creeds so that the chosen Bible is regulated in its reading. Such is Protestantism, and the Church has its very important role of gathering and ordering.
That's where the Unitarians eventually parted company, because to have ordinary comprehension is to start to undo things from below. You notice the inconsistencies that the trinitarian Church filter glosses over or simply refuses to see. The biggest is the Trinity itself: its doctrine is missing from the Bible, and indeed to have it calls for the Church to be that filter. If one goes by the synoptic gospels, Jesus is quite human if God's chosen prophet, with only hints of divinity from Mark; the Gospel of John with its subordinate passages about Jesus is thus Arian, and Paul has Jesus as God's chosen sole worker, the means through which salvation is gained as well as the person who will bring in the Kingdom and (at first) soon. The Bible also veers between God knowing all and saving believers, and God responding to faith and loving to save all.
Much of this is obvious just by reading it, but Martineau writes after biblical criticism comes in (and in Germany too - many Unitarians went to Germany to learn first hand). Biblical criticism is about the why and how these passages vary, and why there is such internal variety in the biblical accounts, and about the dating that shows how Paul affects pretty much everything of significance in the gospels and beyond.
Martineau also writes after it is established that Unitarianism changes over time, and that this is how it now understands its creedlessness. He also writes from the perspective of the broad Church Unitarian, dismissive of the denominationalism of the older biblical Unitarian. Yet the liturgical, conservative Martineau could not give up the Jesus-using basis of much worship. Others around him saw the implications of a religious humanism and multi-faith approach, as with the theist Francis William Newman.
For someone like me, the compulsion of collective liturgy collapses under the individualism, as does the Church. The broad 'pantheistic' Church ceases to be Church, in the end. The binary opposite of Church-individual undergoes a collapse. The Church can only survive as a canvas on to which individuals and groups can paint their own liturgies and be inspired from across the religious, artistic, social-scientific and scientific universe. This is post-Protstant and also Post-Catholic. It is the category Ernst Troeltsch called Mysticism (alongside Church and Sect) and it is inhabited by Unitarians, Quakers and off-the-edge post-Christians.
So the answer is that Unitarians are not Protestant any more, whether or not they are proud of it.