Your analogy seems flawed. Calling a cat a dog is clearly a statement that can be disproved by the scientific definition of what a cat or dog is. Using DNA etc.
However, do you believe that the first apostles understood the trinity? Yes, Simon Peter announced what he did know, which was that Jesus was the Messiah, the Son of the living God, but do you really believe that they fully understood the trinity? Would you dare to not call them Christians?
I do believe the apostles understood the trinity, why else would they baptise in the name of the "Father, and the Son, and the Holy Spirit…ie the trinity.
My analogy was in reference to the theory of relativism, not whether someone is Christian or not.
Full Definition of RELATIVISM
a : a theory that knowledge is* relative to the limited nature of the mind** and the conditions of knowing
b : a view that ethical truths depend on the individuals and groups holding them
*
From Wikipedia:
*Catholic Church and relativism[edit]
The Catholic Church, especially under John Paul II and Pope Benedict XVI, has identified relativism as one of the most significant problems for faith and morals today.[15]
According to the Church and to some theologians, relativism, as a denial of absolute truth, leads to moral license and a denial of the possibility of sin and of God. Whether moral or epistemological, relativism constitutes a denial of the capacity of the human mind and reason to arrive at truth. Truth, according to Catholic theologians and philosophers (following Aristotle) consists of adequatio rei et intellectus, the correspondence of the mind and reality. Another way of putting it states that the mind has the same form as reality. This means when the form of the computer in front of someone (the type, color, shape, capacity, etc.) is also the form that is in their mind, then what they know is true because their mind corresponds to objective reality.
The denial of an absolute reference, of an axis mundi, denies God, who equates to Absolute Truth, according to these Christian theologians. They link relativism to secularism, an obstruction of religion in human life.
Leo XIII[edit]
Pope Leo XIII (1810–1903) was the first known Pope to use the word relativism in the encyclical Humanum genus (1884). Leo XIII condemned Freemasonry and claimed that its philosophical and political system was largely based on relativism.[16]
John Paul II[edit]
John Paul II in Veritatis Splendor
As is immediately evident, the crisis of truth is not unconnected with this development. Once the idea of a universal truth about the good, knowable by human reason, is lost, inevitably the notion of conscience also changes. Conscience is no longer considered in its primordial reality as an act of a person’s intelligence, the function of which is to apply the universal knowledge of the good in a specific situation and thus to express a judgment about the right conduct to be chosen here and now. Instead, there is a tendency to grant to the individual conscience the prerogative of independently determining the criteria of good and evil and then acting accordingly. Such an outlook is quite congenial to an individualist ethic, wherein each individual is faced with his own truth, different from the truth of others. Taken to its extreme consequences, this individualism leads to a denial of the very idea of human nature.
In Evangelium Vitae (The Gospel of Life), he says:
Freedom negates and destroys itself, and becomes a factor leading to the destruction of others, when it no longer recognizes and respects its essential link with the truth. When freedom, out of a desire to emancipate itself from all forms of tradition and authority, shuts out even the most obvious evidence of an objective and universal truth, which is the foundation of personal and social life, then the person ends up by no longer taking as the sole and indisputable point of reference for his own choices the truth about good and evil, but only his subjective and changeable opinion or, indeed, his selfish interest and whim.
Benedict XVI[edit]*