How non believers may view Christian's.

In terms of differences with Christian denominations these are over more minor doctrines, or really over largely the question of authority. This is why the 3 points listed in Post #4 (Jesus life as explained in the Apostle's Creed, the trinity doctrine describing God as explained in the Athanasian Creed, and holding the Bible as the divinely inspired religious text of Christianity) are really the main unifier and way to distinguish a legitimate Christian denomination from either a pagan religion or a heretical sect. All valid Christians are unified as a whole Christian religion in that they hold the 3 beliefs listed.

A 4th perhaps side point that is sometimes made is that a valid denomination should have a historical link to the apostolic succession as well to distinguish it from a more modern cult or a passing movement that comes and goes in the course of history. The historical link to the apostolic succession gives a sort of objective chain from the apostles in the Bible to the modern day as opposed to a newfound and questionable denomination that claims to have some new revelation to try to justify them bringing a different gospel typically to the worldly benefit of one person (a cult leader) or a group of people or political movement. Though one could even consider this something of a moot point since most newfound denominations that do not have a historical link to the apostles also tend to reject one or more of the three core beliefs of Christianity and therefore they could be considerred wholly different religions or elsewise heretical to the point of being outside of the unity of Christianity (ie: islam, jehovah's witnesses, mormonism, etc.)

They are free to call themselves whatever they want, just as you are free to go around pointing a finger and saying they are not REAL Christians.

Frankly what I've had quite enough of is people running around trying to call other people out as fakes. Everybody's trying to play watchdog, or maybe measuring stick, trying to ascertain whether everybody else is a real Christian or not.

I got all I can handle making sure I'm a Christian. So do the people I might criticize for not being real christians. They probably don't need my help and I certainly don't have the time to measure out their lives AND mine.

And the next time someone tells me how not-Christian some alleged Christians are, I'm going to get very sarcastic and very fault finding with the person trying to do the measuring. Best way to shut up a nitpicker is to pick a few of his own nits and hold them up for inspection.

I agree with this, or else one become misguided. We have books to connect us with teaching through apostolic succession. We dont need the establishment. All they have is books too.

Yea, the point on the historical link to the apostolic succession is more or less a guard against cults that claim to be Christian, especially in our time era. Though again this point is somewhat of a more background point since really the 3 core beliefs are the most important points of detailing absolute unity of Christianity as a religion and frankly cults that have no clear historical link to the apostolic succession are probably just going to deny one or all of the 3 major points anyways. A good example of this is the mormons, not only do they have no historical link to the apostolic succession, being founded pretty much out of thin air and can only really trace their religion back to Joseph Smith solely in history, but they obviously deny the trinity doctrine, so even without consulting to their history it is obvious they are outside of the unity of Christianity.

Nicene creed sums it all up.

Nicene creed sums it all up.

It all comes down to the wheat and the tares, without forgetting the field is the world.
I had a sort of melancholy professor in a philosophy class who related his having left his faith behind in the Catholic religion. Coming to exercise he gave us for comment was in response to a philosopher who seemed to me to have it 'right' concerning his main focus on what he called the 'truth with a capital T." So right it seemed to me that I researched the author having been intrigued to perhaps find more material from him (interested in his religious affiliation no doubt though I found no explicit mention of it). However, what I found was that, ultimately, he had hanged himself, and this is what I determined to address in my graded commentary, that this particular man seemed wise about the hope that finding the 'capital T truth' provides except that the despairing 'last word' message he left by hanging himself seemed to contradict all that he'd previously asserted. And I left off with the question of whether he truly believed what he preached. Although I did not actually intend it for the resulting effect on my professor but, nonetheless, I can't forget his notes to me that I'd given him pause to revisit the reality of his own faith.
There is the possibility that the mentioned author came to despair because it didn't seem that anyone else was following his otherwise undeniably wise thinking, but that would've amounted to rejecting an aspect of the capital T truth just as much, considering that the truth (with a capital T) is as it stands regardless of whether the rest of the world agrees.