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A Buddhis Ethic [should be practiced] Without Karmic Rebirth...

at least for Soto Zen understanding.

Zen insist in "doing just because..." just because a true Buddhist practice should be done in this way. Setting Karmic Rebirth ends in a selfish practice as is more less explained by Winston L. King article:

In fact Jones finds some of the motivations in the developed Theravāda tradition that speak of the "good" next life to be gained by "good" actions, to be totally anti-Buddhists because they pander to greed and pride[...]

And not just greed and pride but again and again hate of what we dislike, attachment for what we like and the ignorance of both deluded states of mind...

In a next paragraph there is depicted the notion that Karma as it is, neutral, as explained here:

The theory of karma is the theory of cause and effect, of action and reaction. Every volitional action produces its effects or results. If a good action produces good effects and a bad action bad effects, it is not justice or reward...but this in virtue of its own nature, its own law.[14]

Such neutrality is important because the good and the bad becomes in wholesome and unwholesome depending not in a social moralism but in the inner mental state and the development of awareness and mindfullness.

About Social Engaged Buddhism:

Not all Western Buddhists would agree with Jones in his delineation of a socially active Buddhism as its proper role. Many look upon Buddhism as a refuge from the wear and tear of daily life and from the frenetic pace of life in the West, not as a bugle call to action.

At least the Zen understanding of this aspect comes when we are told "to be in the world but not of the world"; that is, the practice of Dharma even in the middle of the crowded and busiest world. Which has a deep meaning... not pretending to be a saviour of world or society but just to practice with a deep commitment what Buddha taught... the rest will come by itself smoothly.