What makes a person the religion they are? For many of us, we're born into a particular faith or denomination. We either blindly follow along, don't follow along, actively choose to believe and practice it, or choose something else.
Sometimes it's more complicated. My father was born Catholic. He attended Catholic schools and went through the Catholic milestones at appropriate times. Then a nasty curve ball was thrown his way in the form of two Mormon missionaries who showed up on his parents' doorstep. His parents were converted to Mormonism and took their large brood of children along with them. What this really accomplished for my father was to take away his belief system without replacing them with anything of substance. You can't take a bright kid who excels in math and science, immerse him in one religion that's not entirely logical, then jerk him out of it and into another one that has even less a foundation in science-based logic, and expect him to emerge with anything resembling an intact conventional religious faith. We're probably lucky that my dad is even as sane as he is. I think he believes in a higher power and that Jesus was one of the good guys. Beyond that, I doubt he has much in the way of religious beliefs. He attends mass with the family and usually even takes communion, but I suspect he does it so that our family can worship together more than any inner sense compels him to do so.
To the outwardly observing person, my father is a Roman Catholic. What is a Catholic, really, or what distinguishes a Catholic from anyone else? In the olden pre-Vatican II days, Catholics could largely be told apart from the non-Catholics by their observance of meatless Fridays. Someone in the know can still tell for the most part during Lent whether or not a person is adherent to Catholic tenets. If one happens to notice a rosary in a person's possession, it's also a pretty good indicator of Catholicism.
Outward manifestations, however, are just that. What really makes a person a Catholic? The bottom line, to my liberal way of thinking, would be whether or not a person considers himself or herself Catholic. Other less subjective markers do exist, however. I heard once that, even more than a belief in the ecclesiastical infallibility of the Pope, which may very well become a moot point for American Catholics in my lifetime, is the issue of transubstantiation. Transubstantiation is the term used to describe the mysterious process by which the bread and wine of communion are literally transformed into the body of Christ while retaining the physical properties of bread and wine. The Protestant churches, as well as a whole lot of Catholics, believe that the representation is symbolic rather than literal. I have no issue with the beliefs of others differing from mine in this regard, as we all need to be free to believe what we believe.
In black and white, even I can say transubstantiation seems a bit far-fetched, but it's OK with me that a very few things I believe cannot be explained scientifically. If a large portion of my belief system were predicated upon things that did not hold up to fact-based inquiry, I would experience major cognitive dissonance. With just a tiny number of beliefs, however, I can write them off as mysteries and probably be happier than I would be if every single thing in my life had to have a logical explanation.
I'm finished for now, but not finished entirely with this topic.