Ahimsa, one can generally say that dogma has a dominant place, and also that any doctrine that derives from an integrated foundation, explicitly stated as integrated in the CCC, is of primary importance in terms of what is called “binding belief.”
(For a discussion of doctrine vs. dogma vs. discipline, visit
catholic.com/quickquestions/what-is-the-difference-between-doctrine-and-dogma
also
catholic.com/tracts/can-dogma-develop
And you should avail yourself of searches on the non-forum section of Catholic Answers for more on this.
A believer cannot deconstruct the Trinity, for example: declare that he believes in the Father and the Son, but not the Holy Spirit (“but after all, I’m a good Catholic.”

) He cannot say that he believes in all but one of the Sacraments. The Sacraments, all of them, are foundational to the life of a believing Catholic. He cannot develop, privately (or align with dissenting theologians), a theology that states that Christ becomes present in the Eucharist by virtue of the community gathered and not independently through the power of the priest confecting the Eucharist. (“Because Father so-and-so or Ph.D. so-and-so describes the concept that way, and that makes sense to me, personally.”) The Eucharist may be best experienced in community, but it is no less real and effectual if no community is present. Priests offer Mass privately (alone) all the time, and transubstantiation takes place. Transubstantiation is an example of a core doctrine which must be believed.
One can look at the Creeds (the Nicene Creed, the Apostle’s Creed – slightly different content, but similar core concepts). These are not exhaustive in terms of dogma (and they do not go into sacramental theology), but they would be an example of some fundamental priorities as to beliefs.
For example, these teachings declare the Church to be “one, holy, Catholic, and apostolic.” A Catholic may not say, “I no longer believe in the Church as holy, because of all the evident pedophilia.” The concept of holiness refers to the inviolate guidance of the Holy Spirit, not the personal sinfulness of Church members on all levels. That Catholic may not further say (in logical sequence) that “because I do not believe the Church is [always] holy [in the personal holiness of all of its leaders], I therefore have legitimate permission to disbelieve doctrine X, Y, and/or Z – or even to throw it all out and construct or rearrange the Catechism according to my personal priorities.”
The faithful Catholic (or those of us trying our sometimes-feeble best to be

) cannot replace faith with subjective reasoning. (Indiividual reason is not an absolute, because our reason is colored by our experience, our circumstances, and our level of education. Our reason is subject to error.) Making sense to “me, personally” is not the standard for assent of the intellect, let alone the will.
One also has to look at the language in the various sections and particular paragraphs of the CCC. When the Church herself is non-commital, the topic will be presented that way – such as the journey of any particular soul after death. The Church affirms definitively The Four Last Things in the discussion of eschatology, and also discusses mortal sin and its morbid consequences on earth and its indicated consequences at death, but never says in the CCC that the Church would know the destination of a person who dies in mortal sin, because she does not know that. To paraphrase, she says,
not a good idea to die in a state of mortal sin which has not been sacramentally absolved. She also says many times in the CCC (and elsewhere) that the mercy of God is infinite and unfathomable, and no human has insight into God’s mercy at the end of a life.
An example of an integrated doctrine which cannot be deconstructed is the doctrine on marriage. The Church’s doctrine on marriage is radical. It cannot be other than one man + one woman, both canonically eligible to be joined in marriage. No Catholic could support same-sex “marriage” and declare such support to be within the field of faithful Catholicity. Those are radically opposed concepts. And the doctrine of marriage is part of an integrated theology of the human person, his or her native gender, the nature of family and procreation, etc. (Not deconstructible.)
But in any case, I agree with PRMerger, in that examples from you would help.