Karma is a Hindu concept that was taken over by Buddhism, because it was needed to contrast with Nirvana, which is the freedom from the wheel of causation by the realization of emptiness. But as explained elsewhere Karma was more or less a trojan horse because it assumed persistent causality that was at odds with the idea of emptiness. This was resolved by the introduction of the two truths doctrine, which is a kind of dualism between dualism and the nondual.
When we ask whether Karma is real we have to understand something of our own linguistic framework. Like Hinduism because it is Indo-european like the Western tradition has Being. Being in classical greek has four aspects called Reality, Truth, Identity, and Presence. Both Being and Existence are oriented toward these aspects. Existence is neither aspect and anti-aspect. Quintessence is a totalized Being which is both aspect and anti-aspect. In normal Being there is either aspect or anti-aspect. Being and Existence are both called standings because they are orientations toward things of the world. Being projects a priori transcendentals on things, while existence is what is there without the projection.
Since Karma is an characteristic of both of Being and Existence according to Buddhism then it is real. But it also has the other aspects and their duals. Karma is true, it is present, and it is identical. In fact we might posit that Karma is the circulation of beings through the aspects and anti-aspects of Being. There are two truths, the truth of Being, and the truth of existence. The truth of existence is that it is empty. The truth of Being is that it is illusory (mara, maya, dukkah). There are two realities, the reality of Being and the reality of existence. The reality of Being is that it is illusory, while the reality of existence is that it is found as it exists without any projections from us on it. There are two identities, the identity of Being which is imaginary such as the persistence of the atman (soul), and the difference of existence which is that it is aggregates in flux. There are two presences, the presence of Being which presents the illusions that we see phenomenologically, and the presence of existence which is just what is there without any valuing of it.
In other words karma is real, identical, true and present, both at the level of Being and Existence. In fact we can say that karma arises from existence and circulates though Being and then destroys itself in Existence again which occurs in Nirvana. In Being there is a substance that persists which supports continuity though time of beings and gives them their various aspects. But existence is neither aspect nor anti-aspect, that is it is still oriented toward aspects but is something other than the aspects as a duality, i.e. it is nondual.
This is hard to talk about in our philosophical tradition and that is because we are set oriented rather than mass oriented. In the hindu tradition that Buddhism inherited there was pervasion logic and an understanding of the mass nature of things, and so it was easy to talk about the pervasion of existence by emptiness and that made sense. But in a set oriented world using syllogistic logic it is much harder to talk about these relations. So that is why we seem to oscillate between identifying existence with anti-aspects and saying it is neither aspect nor anti-aspect. If existence is empty then it is impossible to pin down conceptually.
But in general we can say that Karma is real by definition whether you are looking at it from the point of view of Being (Sat) or Existence as empty (Asat).