Fraternity is the cornerstone of all organisations, especially those which deal with the occult. It is one of the primary reasons any of us join an Order (or any community) in the first place. To be fraternal is to treat others as a Brother or Sister, and, while this means to do so in the spiritual sense, we need to examine the biological aspect to understand exactly how it works. A physical brother or sister may, for example, be annoying, insulting, or any other denigratory term one wishes to apply; however, they are still one's flesh and blood and a certain platonic love is extended (or should be) even at the worst of times, while the closeness that can occur between biological siblings is a testament to the fraternal bonds that can be formed in the best of times. So should it be for us spiritual siblings.
Thus a basic civility and compassion is required, often more than we would extend to someone not within the Order, for we are bound by oath and mutual aims, and there is a common understanding between us all. This is not to say that we must always agree with one another or blindly obey whatever directions we are given, but rather that if we do have such disagreements that we would attempt to broach them in a way that encourages our fraternal bonds as opposed to straining or severing them.
While ultimately the Golden Dawn is all about magic, it is important to recognise just how valued the aspect of fraternity is, and how, indeed, it acts as the foundation upon which we make our magic, since we work a system that is largely dependant on the coming together of magicians.
The Oath taken in 0=0 is explicit about the fraternal relations required of initiates:
"I undertake to maintain a kindly and benevolent relation with all the Fratres and Sorores of this Order."
While it says "this Order" I believe this "kindly and benevolent relation" should be extended to all people working with the Golden Dawn system, and, dare I say it, to humanity as a whole.
The Obligation of the 5=6 also reinforces the pledge of fraternity in the section dedicated to Hod:
"I further promise ... that I will always display brotherly love and forbearance towards the members of the whole Order, neither slandering nor evil-speaking, nor repeating nor tale-bearing, whereby strife and ill-feeling may be engendered."
Then again in a letter dated 2nd April 1900 Mathers states that "the first duty of an Occultist ... is Fraternity and Fidelity." One cannot get much more explicit than that.
Thus fraternity is one of the basic tennets upon which the Golden Dawn was founded, and it should underscore all other elements of the Work. When we omit this we hack away at the foundations of the Order and of all good human interaction.