What *is* intrinsically real? Is the "unconditioned", "absolute", or "ultimate" intrinsically real? To better see the relative, insubstantial nature of phenomena, maybe it is helpful to think about this another way, that is, seeing what is not relative, not conditioned, not empty.

It has been said that all phenomena are conditioned, not intrinsically real, empty of independent, self-existence. 

What is intrinsically real?  Is nibbāna intrinsically real?


  O bhikkhus, what is the Absolute (Asaṃkhata, Unconditioned)? It is, O
  bhikkhus, the extinction of desire (rāgakkhayo) the extinction of
  hatred (dosakkhayo), the extinction of illusion (mohakkhayo). This, O
  bhikkhus, is called the Absolute


When the terms unconditioned, absolute, and ultimate are used, as in the above and below quotes, do they not mean the same as intrinsically real? Does un-conditioned not mean "independent of conditions" and hence self-existing?


  Bodhicitta literally means “awakened heart.” On the relative level it
  is compassion, expressed in the bodhisattva vow to save all beings; it
  is the aspiration to awaken from ignorance in order to live one’s life
  for the benefit of all. On the ultimate level, bodhicitta goes beyond
  the concepts of self and other. It is the empty, aware nature of the
  mind itself.




The first draft of this question was partly motivated by the question, "is compassion real?", however, from reading One Dharma: The Emerging Western Buddhism (Joseph Goldstein), my understanding is now that compassion is relative (not intrinsically real), i.e. as Joseph Goldstein puts it:


  I realized that the relative level is the expression of the ultimate:
  compassion is the activity of emptiness.


Since that part of my question has been answered, it has now been revised.
You can't walk under a rainbow - in this sense it is an illusion. And yet rainbow is a meteorological phenomenon that actually occurs - in this sense it is not an illusion.

In Mahayana Buddhism we say that the rainbow is "empty". Meaning, if we disassemble it, there is nothing inside, no core, no secret ingredient. If we examine it closely, we will see the water droplets, the sunlight, the reflection, refraction, dispersion, and the observer looking at it from a certain angle - all these things combined lead to appearance of an arch in the sky - but in actuality there is no arch. 

When you see a homeless person, and out of pity give him money for food - on one hand that's real metta-karuna operating in you. On the other hand, giving him money won't really change anything. Perhaps it actually makes it worse, by enabling him to buy alcohol. Perhaps if you took him home by force and taught Dharma - that would be actual help, but you don't do that. So maybe it's not metta, maybe it's ignorance operating in you. Or perhaps, who knows - may be the homeless person should feel pity for you, because he can wander unfettered and you have to go to work every day. In that sense, maybe it's not metta, maybe it's conceit operating in you. In that sense, our metta is not real. Who can judge whether our kindness is real kindness or fake kindness? It depends on the judge. And yet we try to be as kind as we can, and as wise as we can. So metta is like rainbow - depends on the object, the situation, and the position of the observer.

According to Mahayana (specifically the part called Madhyamaka - "the meaning of the middle way"), everything is like that: on one hand it's real - and on the other hand it's not; on one hand it exists - and on the other hand it's an illusion; it looks solid from afar - but falls apart under careful examination. Nothing is real - and yet everything is real.

They say even this ^^^ understanding above is not "real", because it is only a conceptual map - and map is never exactly the same as the territory. 

In this sense nothing is intrinsically real. All our experiences are like "rainbows" in some sense. All our concepts are like "maps". Even Nirvana is just a word that gives a label but does not really explain anything. Entire Dharma is a map or a guidebook that only approximately explains what happens in real life.

In Mahayana we say that going beyond these rainbows and maps (="Realizing Emptiness"), is a big step towards Enlightenment.

Now, depending on a particular school we either say that the actual "ground reality" beyond the rainbows and maps (=ontological reality behind experiences and descriptions) is intrinsically real. OR we say that there is no such absolute ground and everything is completely relative. If you belong to Nyingma or Kagyu - then you say that the ground reality is real, just indescribable and not accessible to direct experience, but we actually are living it. And if you belong to Gelug, then you say that this ground is only an abstraction in our mind, leaving us with nothing to stand on. This is known as 
the Rangtong-Shentong distinction.