Hi!
These are interesting topics, which is why I am responding.
I have had long association with the NKT (about 15 years) and have also had the chance to take part in many events and read many books by other traditions, such as FWBO, FPMT, Diamond Way and some others. Like the monk one of you wrote about, I am a huge fan of Chokyam Trungpa, as well as many similar authors like J. Krishnamurti.
Generally, I never encountered any opposition within the NKT regarding my love of other books. I have openly spoken to members about my dislike of the way in which the whole Dorje Shugden issue is being treated, and openly voiced my doubts concerning many teachings. Most of these have been met with interest, openess and a willingness to engage in discussion.
Behind closed doors however, as with any one of the above mentioned Buddhist traditions, there is a very harsh iron fist controlling the institutional traits of the NKT. Some ‘higher’ personell of the head office generally try to run the tradition in a very ridgid way, surpressing any questioning, discussion or alternative views. I have long since made up my mind not to get involved with that aspect, and I don’t allow it to bother me in the slightest. It is human nature: the need to identify with some kind of group and zealously protect it. Along those lines, I have to say that I have been kicked out of a Tibetan shop in Zurich once after the owner gathered that Geshe Kelsang was one of my teachers…
From what I know, and in my own opinion, these problems are more likely caused by a kind of committee of people in charge of admin, business and organisation within the tradition, rather than by Geshe Kelsang or whoever the root Guru of the respective tradition may be.
For me, the bottom line is always this: You must be your own spiritual guide, you must find your own way and you must remain open to truth/Dharma. If we attach ourselves to any tradition and conclude that we have found ‘the path’, then we close ourselves to actual spirituality. This issue is more about confusing institution with actual dharma; or as Trungpa calls it, ‘spiritual materialism’.
I see several new people here, so welcome to the forum! And thank you for your good attitude. At AYP it is about practices that work based upon a lot of people trying them, and not about holding on to anything because of ego or tradition. 
This may be of interest to subsequent readers of this thread.
I have taken a look at: http://www.iivs.de/~iivs01311/SDLE/Contents.htm, and it appears to be a relatively unbiased source.
Some observations
It appears that Tibetan in-fighting has deep and historical roots.
The fighting is done on physical, political, and magical levels.
The magical fighting is considered to be just as real as the other two, and is monitored via dreams and oracles.
At the magical level, it is most likely believed that reducing the number of Shugden worshippers will reduce the strength of that deity’s ability to attack the Dalai Lama in his attempt to integrate the various sects.
As the efficacy of our meditation is moderated by our intent and attitude, the choice of one protector deity over another can be irrelevant to progress along the way. In the Tibetan systems, magical techniques are primarily used during the purification process to subdue or eliminate emotional and desire based mental content, but these become less relevant once meditation has been achieved.
The main danger is in whether we become enmeshed in magical workings directed at material or political aims, rather than meditation.
It seems to me that Tibetan ways are being challenged to adapt to a more open world, which is itself attempting to become more co-operative, and we are seeing the effects of that challenge. I think sulmaya’s post also sums it up well.
Some supporting excerpts and paraphrases from the link above follow:
History
In earlier times Pehar reigned as war god of the Hor Mongols. According to the sagas, this wild tribe was counted among the bitterest opponents of the pre-Buddhist Tibetans. After terrible battles the Tibetan national hero defeated the rapacious Hors, and won their commitment and that of their chief god, Pehar, with an eternal oath of loyalty. Padmasambhava magically mastered Pehar, who was thus “Buddhized”, and 900 years later, the “Great Fifth” Lama pressed the former war god of the Hor into service as the state oracle.
The Tibetan state oracle (Nechung Lama) is one of the most highly respected and influential lamas in the Tibetan state.
The Tibetans can be described without exaggeration as being “addicted to oracles”, and the Dalai Lama is known not to take important decisions of state without first consulting the State Oracle. The deity conjured up is called Pehar.
Drakpa Gyaltsen, the abbot of the powerful Drepung (Yellow Hat) monastery, organized a rebellion against the “Great Fifth” lama, but was discovered and eliminated. After his death he transformed into a warlike martial spirit and took on the fearsome name of Dorje Shugden.
A group within the Yellow Hat (Gelugpa) order, used magical and political means to gain the supremacy of their order. They elevated Dorje Shugden into a position as a protective deity of their group.
Politics
Since 1996 at the latest, Pehar and his Nechung medium have met with embittered competition from among the Tibetan’s own ranks. This is in the matter of the tutelary and divinatory deity, Dorje Shugden.
It is primarily conservative circles among the Gelugpas (the “Yellow Hats”) who have grouped around this figure. They demand the exclusive supremacy of the yellow sect (the Gelugpas) over the other Buddhist schools.
This traditional political position of the Shugden worshippers is not acceptable to the Fourteenth Dalai Lama (although he himself is a member of the yellow sect) because he is working towards an integration of all Tibet’s religious orientations, including the Bonpos.
Struggle
In 1976 the Fourteenth Dalai Lama (Kundun) declared that he did not wish for his person to associated in any way with Dorje Shugden, especially because the worship of this “reactionary” spirit had come into conflict with three other dharmapalas (tutelary gods) which he revered highly, the oracle god Pehar, the terrible Palden Lhamo, and the protective god Dharmaraja.
Rumors report of a dream of the Kundun in which Shugden and Pehar had fought with one another.
On a number of occasions Pehar prophesied via the Nechung Lama that Shugden was attempting to undermine the sovereignty of the Kundun.
The following statement by the Kundun has been leaked from a secret meeting of influential exiled Tibetan politicians and high lamas which the Dalai Lama called to discuss the Shugden case in Caux (Switzerland): “Everyone who is affiliated with the Tibetan Society of Ganden Phodrang government (Tibetan Government) should relinquish ties with Dhogyal (Shugden). This is necessary since it poses danger to the religious and temporal situation in Tibet.
Namaste