The New Kadampa Tradition (NKT) is neither sectarian nor intolerant because it actively respects all religions and people’s right to practice however they wish. There are many good reasons why different people want and need different spiritual traditions (or no tradition). As Ven Geshe Kelsang says:

Each tradition has its own uncommon good qualities, and it is important not to lose these.

The NKT-IKBU studies and practices its own tradition but sincerely respects other spiritual traditions – this point is included in the NKT Internal Rule 8§3 

Sectarianism is discriminating against another tradition, religion, or school. It implies being bigoted or narrow-minded. Non-sectarian does not mean practicing all traditions, but having respect for all traditions and not criticizing them.

The NKT was marginalized by some into a “sect”, as opposed to a part of mainstream Buddhism, when the 14th Dalai Lama said publicly and with no valid reason that Dorje Shugden practice promotes sectarianism. Paradoxically, he was, at the time, unlawfully enforcing a ban on a nearly 400-year-old religious tradition.

From an interview with Geshe Kelsang Gyatso with Donald Lopez Jr in Tricycle Magazine, Spring 1998:

LOPEZ: Given your devotion to Dorje Shugden and your founding of the New Kadampa Tradition, do you feel that Je Tsongkhapa’s view, meditation, and practice is the most complete in all Tibetan Buddhism? Is it only through Je Tsongkhapa’s teachings that one can attain enlightenment? Or is it also possible through Nyingma or Kagyu?

GESHE KELSANG GYATSO: Of course! Of course we believe that every Nyingma and Kagyupa have their complete path. Not only Gelugpa. I believe that Nyingmapas have a complete path. Of course, Kagyupas are very special. We very much appreciate the example of Marpa and Milarepa [in the Kagyu lineage]. Milarepa showed the best example of Guru devotion. Of course the Kagyupas as well as the Nyingmapas and the Sakyupas, have a complete path to enlightenment. Many Nyingmapas and Kagyupas practice very sincerely and are not just studying intellectually. I think that some Gelugpa practitioners need to follow their practical example. But we don’t need to mix our traditions. Each tradition has its own uncommon good qualities, and it is important not to lose these. We should concentrate on our own tradition and maintain the good qualities of our tradition, but we should always keep good relations with each other and never argue or criticize each other. What I would like to request is that we should improve our traditions while maintaining good relations with each other.

Ven. Geshe Kelsang has taught that the most effective method to gain spiritual realizations is to practice one tradition sincerely without mixing. Just as people have the right to mix traditions if they wish, and should not be criticized for doing this, others should also have the right to practice one tradition without being criticized.

By emphasizing one tradition sincerely, the NKT is not saying that it is better than other traditions; just that this method works the best for those of this tradition. As Mahayanists who understand that living beings need to be helped in different ways according to their differing karmic inclinations, the NKT never says that it is the best and that other traditions are inferior. Rather, the NKT respects and appreciates other traditions, and refrains from criticizing them. In this way, the NKT is non-sectarian.

As it says in How to Understand the Mind: the Nature and Power of the Mind:

Every Teacher and every tradition has a slightly different approach and employs different methods. The practices taught by one Teacher will differ from those taught by another, and if we try to combine them we will become confused, develop doubts, and lose direction. If we try to create a synthesis of different traditions we will destroy the special power of each and be left only with a mishmash of our own making that will be a source of confusion and doubt. Having chosen our tradition and our daily practices we should rely upon them single-pointedly, never allowing dissatisfaction to arise. At the same time as cherishing our own tradition we should respect all other traditions and the right of each individual to follow the tradition of their choosing. This approach leads to harmony and tolerance. It is mixing different religious traditions that causes sectarianism.