There is no transgression in the other traditions when they talk to Thaye Dorje, who is the person duly recognized by the Kagyu lama Shamar Rinpoche; the reason the Dalai Lama's government (CTA) doesn't do this is because the Dalai Lama wrongly interfered with the Karmapa recognition in the first place; the Dalai Lama doesn't like spiritual or political rivals; he wanted to merge all 4 schools under his own command, but was met with opposition by the 16th Karmapa, and other high lamas as well.
So, in other schools, the issue is that I think it is very noticeable when the Dalai Lama tries to take over their school. In the Gelugpa school, it is difficult for him to be as in charge as he would like; there are much better and more important spiritual guides than he, such as the root guru he disavowed, Trijang Rinpoche. So, if the Dalai Lama wants to be in control spiritually, he needs to divide groups, lie, and control people himself. If he picks whomever he wants for Karmapa (anyone but the one that the rightful lineage head of the Kagyus picked) then he can pretend he's in charge of the Kagyu school, can pretend that he's choosing their leader, etc.. People won't believe him as much, because there has been a long standing issue that the Dalai Lamas of Tibet, from especially the time of the Evil 5th Dalai Lama, always considered the Kagyus rivals, and would (in the time of the 5th Dalai) kill thousands of monks, behead hundreds and hundreds of abbots, and then forcibly convert Kagyu monestaries. The Kagyus are wise to the nonsense of the Dalai; he has done this in many recognitions, because the Kagyus were powerful, and he doesn't like rivals.
Concerning the Shugden prayers, how on earth could a mere politician compete spiritually with Trijang Rinpoche? People respected Trijang Rinpoche, and rightly so; how would the Dalai Lama eclipse the power of Trijang Rinpoche? One way is to ban Trijang Rinpoche's practice, demonizing it so that anyone who supports highly realized Shugden lamas will be split and fragmented. Then the Dalai Lama downgraded the most important Gelugpa lama of that era to the status of his 'junior tutor.'
The Dalai Lama plays the west against the east, giving misinformation to both sides, because not very many people know the history of Tibet, or much about Buddhism at all. He is able to lie about his root guru, downgrading him only to junior tutor status; he keeps trying to make everyone think he is in charge of Buddhism, but people like the 16th Karmapa weren't having it. It's fine for lamas to meet with the real Karmapa (Thaye Dorje); the reason the Dalai Lama can ban Shugden in his own school, is that it is the most politicized of the schools, due to H.H. DL's being involved in running the country and running that school; people in that school have found it unwise to speak out; the Kagyus and other high lamas know the Dalai Lama isn't in charge of their schools, so they just won't listen to them. The Dalai Lama is more evil to Shugden followers because rivals in his school would be more important than he, and he can't look less important on his own turf, or how will he ever take over Buddhism?