What denominations apply the doctrine Nuda Scriptura?

Historical background of Solo/Nuda Scriptura

Keith Mathison wrote a paper Solo Scriptura: The Difference a Vowel Makes published in the journal Modern Reformation Vol 16 Issue 2 (March/April 2007) to contrast Solo vs. Sola Scriptura. He also wrote the 2001 well-cited book The Shape of Sola Scriptura whose table of contents can be found here. His description of "Solo Scriptura" origin and motivation seem to match your definition of Nuda Scriptura.

Quote from Keith's paper:

In contrast with the Reformation doctrine of sola Scriptura, the revisionist doctrine of “solo” Scriptura is marked by radical individualism and a rejection of the authority of the church and the ecumenical creeds. If we compare the statements made by advocates of “solo” Scriptura with the statements of Reformational Christians above, the difference is immediately evident. It is also important to observe the source of this doctrine in early America. As Nathan O. Hatch notes, the first Americans to push the right of private judgment over against the church and the creeds were unorthodox ministers.

The liberal minister SimeonHoward (1733-1804), for example, advised pastors to “lay aside all attachment to human systems, all partiality to names, councils and churches, and honestly inquire, what saith the Scriptures?” In his own effort to overturn orthodox Christianity,Charles Beecher (1815-1900) denounced “creed power” and argued for “the Bible, the whole Bible, and nothing but the Bible.” The universalist minister A. B. Grosh (d. 1884) declared in a similar way, “In religious faith we have but one Father and one Master, and the Bible, the Bible, is our only acknowledged creed book.”

The radical American version of “solo” Scriptura reached its fullest expression in the writings of the Restorationists as they applied the principles of Democratic populism to Enlightenment Christianity. In 1809, the Restorationist Elias Smith (1769-1846) proclaimed, “Venture to be as independent in things of religion, as those which respect the government in which you live.” Barton Stone (1772-1844) declared that the past should be “consigned to the rubbish heap upon which Christ was crucified.” Alexander Campbell (1788-1866) made his individualistic view of Scripture very clear, declaring, “I have endeavored to read the Scriptures as though no one had read them before me, and I am as much on my guard against reading them to-day, through the medium of my own views yesterday, or a week ago, as I am against being influenced by any foreign name, authority, or system whatever.” As the Reformed Princetontheologian Samuel Miller (1769-1850) rightly observed,“themost zealous opposers [of creeds] have generally been latitudinarians and heretics.”

Another resource that talks about the kind of Christians holding Solo/Nuda Scriptura can be found in this short the blog article Sola Scriptura or Nuda Scriptura?. Quote:

... proponents of NS are themselves confessional Christians of a sort; they just don’t realize it. If you were to ask one to summarize in a sentence or two who Jesus is and why he came to earth, they would, by necessity, need to produce a condensed statement of the relevant points of doctrine in order to answer the question, i.e., produce a confession. The difference between this confession and a standard historic confession is that one was deliberated on, debated, and prayerfully considered by many intelligent, God-fearing men, and the other was not. One such confession has stood the test of time and the scrutiny of generations of believers from all walks of life, the other has not. The fact of the matter is, proponents of NS already have a confession. The question then becomes, is their confession the product of an individual or a very narrow sect, or is it the product of hundreds of years of diligent study, discussion, prayer, and reflection?

Solo/Nuda Scriptura compared with Biblicism

A related issue with Bible Interpretation is Biblicism which also rejects historic creed / confession, but may differ from Solo/Nuda Scriptura in its tendency to reject general revelation and "narrows the scope of its application to only that which the Bible explicitly states and not to that which it implies as well." (quote from chapter 2 of The Case for Traditional Protestantism).

Michael Bird, a well-published Australian evangelical theologian, offered his definition of Biblicism in a Aug 2020 blog article What is Biblicism? then proceeded to contrast it with proper understanding of Sola Scriptura:

Let me say that biblicism is definitely not the Protestant view!

When the Reformers and their progeny articulated Sola Scripture, it did not mean the naked Scripture, mere Scripture, but more like the primacy of Scripture alongside tradition, experience, and nature, etc.

When Protestants articulated the clarity of Scripture, they did not mean all of Scripture was equally clear, but that Scripture was clear when it came to the gospel and salvation, beyond that, one might need a Philip to run beside one’s chariot and to help you explain this or that in your Bible.

When Protestants articulated the sufficiency of Scripture, it was not sufficient to deal with things beyond the Bible’s own subject of discourse, like open-heart surgery, treating bipolar disorder, or macro-economics. The Bible might have values, principles, and affirmations that contribute to these things, but they are not sufficient to deal with them in their entirety.

When Protestants spoke of the authority of Scripture, they meant the authority of the Holy Spirit speaking in Scripture, the same Spirit who was part of the triune economy, who illuminates believers into the truth, who raises up pastors and teachers for the church, and who animates its creedal and liturgical heritage.

Proper practice of Sola Scriptura as Primacy of Scripture

In a blog article Sola Scriptura Then And Now adapted from a paper he delivered earlier at "The Global Impact of the Reformation" conference in Oct 2017, Don Carson shared eight reflections on sola Scriptura, "reflections that are variously historical, theological, and pastoral." Quote from Reflection #4 (on how Reformed tradition respects the authority of the creeds but places them under Scripture):

4. Sola, Not Solo or Nuda

One cannot too strongly insist that sola scriptura is not to be confused with solo scriptura or nuda scriptura. The doctrine does not open itself to biblicist proof-texting that is devoid of awareness of how Scripture has been read and applied in past generations and in other cultures. As John Peckham astutely comments, “All that is necessary to undergird the ‘sola’ of this principle is for Scripture to present itself as uniquely authoritative over all other factors. Notably, each of the three categories that encompass other possible sources of theology—reason, experience, and tradition—are not excluded but are explicitly subordinated to the unique authority of Scripture.”

...

When we speak of other authorities, such as creeds and confessions (for example, Augsburg, Heidelberg, Westminster), their authority does not subtract from the authority of Scripture, as if by acknowledging their authority, the authority of Scripture is correspondingly reduced. We are not playing a zero-sum game. The authority of the creeds is always a subordinate and derived authority. The authority of a creed invariably leaves the sola of sola scriptura unscathed, because Scripture alone has the authority of the norma normans.[2]

Much more evidence could be adduced to justify a place for creeds, formulas, catechisms, and more. But Christians in the Reformed tradition are not living up to the best insights of the Reformation when confessional documents are given such status that they effectively stand over Scripture, instead of under it.

Summary

The ones who adhere to Nuda Scriptura are those who interpret the Bible with radical individualism and who reject the authority of the church and the ecumenical creeds. They in effect write their own confessional statements from scratch.

They are to be contrasted with Protestant denominations which base their teachings on the 16th century Reformers whose view were in turn Sola Scriptura properly understood.

Another contrast is with non-denominational churches which respect a historic creed (such as the 381 Nicene Creed) and/or a historic confessional statements (such as the 1647 Westminster Confession of Faith) while maintaining Sola Scriptura (see Don Carson's paper quoted above on how they do this).