As “radical” as they seem, they are grounded in classic Mahayana Buddhism, which, though different in numerous ways from EBT Buddhism, is not “new age” at all and is very closely grounded in sila. Just open up any basic exposition on Mahamudra (Tashi Namgyal’s Moonbeams for example) or Dzogchen (Jigme Lingpa etc) and you will see a pretty standard Mahayana ethical and intellectual framework as its foundation. This foundation is, though unique in its own ways, still based on common Buddhist ideas, like the four brahmaviharas and the 10 wholesome karma paths. Indeed, that basic framework is what figures who brought Buddhism to Tibet, such as Atisha and Shantarakshita, focused on. So, your assertion that these systems are based “solely on the view of emptiness” is just false.
As a further example, the Dalai Lama is known also as a Dzogchen practitioner (as have many other Dalai Lamas in the past), would you say that the man who spends most of his time teaching about compassion, kindness and virtue is following a “new age” teaching that lacks ethics and only teaches emptiness?
Honestly, if Buddhists can’t get along without smearing each other’s traditions, we are in deep trouble.