HHDL's motivation is beyond question or comprehension. We cannot really use our tainted explanations of theories as to why this or the other is said or done. We simply cannot! If we trust HHDL to be who he is, an emanation of Avalokiteshvara, then we certainly cannot question the motives let alone the reasoning behind it.
Leave your rational mind at the door? This is not what Buddha taught. He taught that we should test everything.
We may not be able to see the motivation behind the Dalai Lama's actions directly, but we can see the result - a schism in the Sangha, families at each other's throats, Shugden practitioners being beaten and discriminated against, Shugden statues being destroyed and general spiritual degeneration.
In short, suffering. There's no evidence that the Dalai Lama is Avalokiteshvara; in fact, quite the opposite I'm sorry to say.
When does a Buddha's actions cause suffering? When do Buddhas disagree with their Spiritual Guides and claim to know better and practise sectarianism towards revered and genuine spiritual practices?
People use these kinds of arguments to justify irrational beliefs such as 'well, we can't really know God, so we cannot say why there is suffering in the world, but if God is the creator, there must be some good reason for it"
It's just the same; please people, we come from a proud lineage of fine logicians such as Dignaga, Dharmakirti, Nagarjuna, Chandrakirti, Shantideva and Lama Tsongkhapa - please don't appeal to the irrational as an explanation for something that you find unexplainable or unpalatable. Aren't we supposed to think for ourselves? It's precisely blind faith that has led to this sectarian ban in the first place - the Dalai Lama's blind faith in the fifth Dalai Lama and his followers blind faith in him.
You are creating a 'bigger picture' - there is no evidence and no logical justification for one. It's simply blind faith.