These issues come up because few people bother to study "Book T" and how Mathers actually used Elemental Dignities. It is the most misunderstood topic in Tarot.
The system was a way for determining how 'strong' (i.e., powerful and important) each card or set of cards was in a reading - and therefore which cards to pay most attention to. It was also a way to eliminate irrelevant cards. It was designed to go with specific spreads in which the cards are read in pairs and triads.
You need to actually lay out the cards he used as examples and follow closely what he did if you want to understand the GD system. For one thing, Mathers used the terms "neutral" and, in a different context "neutralize," and they signify two different but important things. Secondly, the term 'friendly' does not mean that the cards act nice toward each other. Any combination can be for 'good or ill' depending on the cards!!!
Here are Mathers' basic rules (see _21 Ways to Read a Tarot Card_ for a more complete explanation):
1) Cards are "Strong" when the suits/elements are the same; they are "very strong for either good or evil, according to their nature."
In other words, two swords cards are like-minded and egg each other on. They can greatly increase either the good or ill in each (depending on their individual meanings).
2) When the suits/elements are both masculine/active or feminine/passive, they are "moderately strong because they are friendly to each other." [Fire+Air; Water+Earth.]
They increase the power and strength of the other, but whether this is good or bad depends on the specific cards.
3) When the suits/elements complement each other, they are "somewhat friendly" (also called neutral). [Fire+Earth; Air+Water.]
They show relatively ineffectual interactions. (Personally, I like to think of them as mild irritants that can be mildly correctional and therapeutic to each other but without great impact as to whether they strengthen or weaken the other.)
4) When the cards are of contrary elements they tend to "weaken each other greatly for good or evil, and neutralize [cancel out] their force." [Fire+Water; Air+Earth.]
In practice, Mathers often cancelled out the effect of cards with contrary elements.
He simply did not read PAIRS that were of contrary elements!! (They could not co-exist in the same room so BOTH would leave.)
In TRIADS, if the two cards flanking a central one were contrary to each other, he simply didn't read those flanking cards but, instead, concentrated on the center card as if it were alone.
However: "If the contrary element is only in one flanking card, then the other becomes a connecting card so that the first
is not weakened, but is modified by the influence of both cards and is, therefore, fairly strong." In other words, the center card overcomes the neutralizing force of its contrary flanking card through the support of a card that is more 'friendly' to it - for good or ill.
If both flanking cards are contrary to the center one then they dominate it completely; the effects of the central card are extremely weak.
People have modified this system to make sense to themselves (and often because they didn't understand the original). It's fine to modify the idea to your own use, just understand that you are doing so, and that none of these adaptations are "right" while others are "wrong." The important thing is what works.
Mary