I think it is no coincidence that the greatest and most impressive lamas of history studied broadly in different traditions. Jamgon Kongtrul Lodro Thaye, the Dalai Lamas, The Karmapas, Gampopa, Lama Tzongkhapa - these great masters looked at a broad corpus of literature. Now surely they did have to make some decisions in terms of their daily practices, where their focus would lie. But they did so after having a broader knowledge of the various sectarian philosophies.
Here at Sera the monks who only study the yig-cha, monastic manuals of their college, who do not devote much time to the Indian treatises and who never look into the opinions of lamas from the other monasteries, are considered to be doing the "bare minimum'.
HH Dalai Lama on a recent visit exhorted the monks to focus on the Nalanda texts themselves, as a Lama's commentary was only one interpretation. Similarly, he said they should investigate themselves what Lama Tzonkhapa said, not what one of the commentators said he said. And then, to look into the forerunners of Tzongkhapa, like Sakya Pandita.
I think the same standard applies in modern education,really. If I am studying at a university and only use the school's texts books, or quote from a few sources, without investigating the other opinions, citing them and integrating them, my essays and presentations would be considered below par.
Let's take Atisha as an example. He held the Madhyamika Prasangika view. His teacher Serlingpa (Suvarnadvipi), did not. Now, if he had the outlook "I will only go to the teachers upholding the view of my (Middle Way) tradition", he would have missed out. Because although he considered Serlingpa to hold a so-called "lower view" of emptiness, he said he was the kindest teacher because it was through his instructions that he was actually able to give rise to bodhicitta.
For myself, the teachings I have received from the Theravada and Kagyu traditions have contributed greatly to my ability to understand, study and translate Gelugpa teachings. It also means that when people from other traditions mention particular views or masters, I don't draw an embarassing blank, as I used to.
The institutional loyalty on which some masters insist for me is a little bit suspect. Because in a university if a professor said "You should only read books by so and so"... he would be censured.
A true master is not threatened by their students learning with others. Fortunately my teachers have always given me that freedom. Focus is one thing, bias is another.
If Lama Tzongkhapa had not studied with a broad variety of masters, would he have been able to produce the vast corpus of literature that he did? If Gampopa had not studied with the Kadampa teachers as well as Milarepa, would he have produced his magnum opus "Jewel Ornament of Liberation". Would Jamyang Kongtrul Lodro Thaye have been able to revive a true and integrative practice tradition that was failing?
History tells us again and again that far from diluting Buddhism, syncretism actually vitalizes it, reinvigorates it.
A foolish man proclaims his qualifications,
A wise man keeps them secret within.
A straw floats on the surface of water,
But a precious gem placed upon it sinks to the depths