Are there any denominations that give official advice on how to handle the uncertainty in their doctrines?

UU (Unitarian Universalist) "Christians" recognize errancy in the Gospels, using scripture only for insight into understanding the concept of God. The UUA (Unitarian Universalist Association) publicly states: "scripture is never the only word, or the final word." [How then is UUA, Christian?] - The Unitarian Universalist Association explains their own perspective of wisdom literature at uua.org:

Most Unitarian Universalist [Christians] believe in God, but not the traditional God-as-Trinity that most Christian churches promote. The UU Christian God is all-loving, as our Universalist forbears taught, and a unity, as our Unitarian forebears taught. This God is too big to be contained in one person, one book, one tradition, or one time in history. To UU Christians, Jesus is an inspiration and his teachings are profound—he possesses a divine spark that is born in all of us, and can be cultivated our whole lives long.

Our congregations celebrate Christmas and Easter with a liberal and inclusive twist. Our style of worship and day of worship are from the Christian tradition, even though our worship draws from many sources. The Bible and its many interpretations have largely shaped our history.

Some of our UU congregations are Christian in orientation, worshipping regularly with the New Testament, offering Communion, and celebrating Christian holidays throughout the year. All of our congregations welcome people with Christian backgrounds and beliefs.

https://www.uua.org/beliefs/what-we-believe/beliefs/christianity

On "Sacred" Texts:

One might say that life is our scripture. While Unitarianism and Universalism both have roots in the Protestant Christian tradition, where the Bible is the sacred text, we now look to additional sources for religious and moral inspiration. Over two centuries, our religious tradition, a “living tradition,” has branched out from its roots. We celebrate the spiritual insights of the world’s religions, recognizing wisdom in many scriptures.

When we read scripture in worship, whether it is the Bible, the Dhammapada, or the Tao Te-Ching, we interpret it as a product of its time and its place. There is wisdom there, and there are inspiring stories, but scripture is not to be interpreted narrowly or oppressively. It can be beautiful, inspirational and wise. But in our tradition, scripture is never the only word, or the final word.

From the beginning we have trusted in the human capacity to use reason and draw conclusions about religion. Influenced by experience, culture, and community, each of us ultimately chooses what is sacred to us.

https://www.uua.org/beliefs/what-we-believe/sacred-texts

Are UU "Christians" all about serving You or God? - That is a totally different question.

Are there any denominations that openly acknowledge the existence of (some) uncertainty in (some of) their doctrines, and provide official advice to their members on how to handle that uncertainty?

Such options do exist in Catholic teachings. At least, if I understand your question correctly.

They are usually based on very specific, yet limited circumstances.

For example the question of evolution? It is permitted for Catholics to accept the theory of evolution over the tradition traditional views of creations.

Pope Pius XII's encyclical of 1950, Humani generis, was the first encyclical to specifically refer to evolution and took up a neutral position, again concentrating on human evolution:

The Church does not forbid that ... research and discussions, on the part of men experienced in both fields, take place with regard to the doctrine of evolution, in as far as it inquires into the origin of the human body as coming from pre-existent and living matter.

Pope Pius XII's teaching can be summarized as follows:

• The question of the origin of man's body from pre-existing and living matter is a legitimate matter of inquiry for natural science.

• Catholics are free to form their own opinions, but they should do so cautiously; they should not confuse fact with conjecture, and they should respect the Church's right to define matters touching on Revelation.

• Catholics must believe, however, that humans have souls created immediately by God. Since the soul is a spiritual substance it is not brought into being through transformation of matter, but directly by God, whence the special uniqueness of each person. All men have descended from an individual, Adam, who has transmitted original sin to all mankind. Catholics may not, therefore, believe in "polygenism", the scientific hypothesis that mankind descended from a group of original humans (that there were many Adams and Eves).

Some theologians believe Pius XII explicitly excludes belief in polygenism as licit. Another interpretation might be this: As we have nowadays in fact models of thinking of how to reconcile polygenism with the original sin, it need not be condemned. The relevant sentence is this:

Now it is in no way apparent how such an opinion (polygenism) can be reconciled with that which the sources of revealed truth and the documents of the Teaching Authority of the Church propose with regard to original sin, which proceeds from a sin actually committed by an individual Adam and which, through generation, is passed on to all and is in everyone as his own. — Pius XII, Humani generis, 37 and footnote refers to Romans 5:12–19; Council of Trent, Session V, Canons 1–4

Evolution and the Catholic Church

Catholic believes in the Assumption of Mary. The definition however does not touch on the question of how or if Mary died. Some believe she was assumed into heaven without dying. However tradition holds she physically died before her her Assumption. Catholics are free to believe either theory, but must hold to the dogma of the Assumption of Mary.

In 1950 Pope Pius XII invoked papal infallibility to define the dogma of the Assumption of the Blessed Virgin in his Apostolic Constitution Munificentissimus Deus:

We proclaim and define it to be a dogma revealed by God that the immaculate Mother of God, Mary ever virgin, when the course of her earthly life was finished, was taken up body and soul into the glory of heaven.

Assumption of Mary

In the dogmatic statement, the phrase "having completed the course of her earthly life" was carefully written to leave open the question of whether or not Mary died before her Assumption, or whether, like the Assumption of the Prophet Elijah, Mary was assumed before death; both possibilities are allowed in the formulation. It is a question of nuance!

When points of dogma are unsure, theologian often speculate on their outcomes. Rome has given us a few guidelines to follow here.

When the dogmatic material with the help of the historical method has been derived from its sources, another momentous task awaits the theologian: the philosophical appreciation, the speculative examination and elucidation of the material brought to light. This is the purpose of the "scholastic" method from which "scholastic theology" takes its name.

The scope of the scholastic method is fourfold:

• to open up completely the content of dogma and to analyze it by means of dialectics;

• to establish a logical connection between the various dogmas and to unite them in a well-knit system;

• to derive new truths, called "theological conclusions" from the premises by syllogistic reasoning;

• to find reasons, analogies, congruous arguments for the dogmas;

But above all to show that the mysteries of faith, though beyond the reach of reason, are not contrary to its laws but can be made acceptable to our intellect. It is evident that the ultimate purpose of these philosophical speculations cannot be to resolve dogma finally into mere natural truths, or to strip the mysteries of their supernatural character, but to explain the truths of faith, to provide for them a philosophical basis, to bring them nearer to the human mind. Faith must ever remain the solid rock-bottom on which reason builds up, and faith in its turn strives after understanding (fides quoerens intellectum). Hence the famous axiom of St. Anselm of Canterbury: Credo ut intellegam. However highly one may esteem the results of positive theology, one thing is certain: the scientific character of dogmatic theology does not rest so much on the exactness of its exegetical and historical proofs as on the philosophical grasp of the content of dogma. But in attempting this task, the theologian cannot look for aid to modern philosophy with its endless confusion, but to the glorious past of his own science. - Dogmatic Theology (Methods of dogmatic theology)

As both scientia and sapientia, theology is not merely an historical undertaking but is a study of the truth concerning God, a task as necessary today as it has been in every age. We aim to recover the study of the theological tradition from those who would relegate it to mere history, and we thereby hope to undertake the pursuit of holy wisdom by following in the footsteps of the Fathers and Doctors of the Catholic Church.