It's just metaphysical speculation. Those aren't exactly prone to truth or falsity evaluations.
The denial of spacetime is a speculation that is in line with theories of certain physicists ("Spacetime is doomed"). Kastrup heavily relies on this particular approach in physics that considers a "top-down" view of physics privileged, as opposed to the "bottom-down" one. In other words, it is the primacy of the observer and observation, and thus, the primacy of consciousness. For example, Hawking and Hertog say:
if one does adopt a bottom-up approach to cosmology [God's eye view], one is
immediately led to an essentially classical framework, in which one
loses all ability to explain cosmology’s central question—why our
universe is the way it is.
The framework we propose is thus more like a top-down approach to
cosmology, where the histories of the universe depend on the precise
And John Wheeler complements this:
Each elementary quantum phenomenon is an elementary act of ‘fact
creation.’ That is incontestable. But is that the only mechanism
needed to create all that is? Is what took place at the big bang the
consequence of billions upon billions of these elementary processes,
these elementary ‘acts of observer-participancy,’ these quantum
phenomena? Have we had the mechanism of creation before our eyes all
this time without recognizing the truth?
That spacetime is not objective but imposed by subjectivity is in accordance with Schopenhauer's views. In the words of Donald Hoffman (who holds similar views):
Spacetime is a data structure that we create to represent fitness
payoffs and how to get them.
Therefore, each observer evolves to have a different interface into [whatever is at the bottom of all of this]. Spacetime and the physical world is an illusion akin to Maya.
Kastrup goes very close to Carlo Rovelli who claims that the world we see is relativistic and up to the perceiver. However, he departs from Rovelli in that he postulates a universal kind of consciousness which is the source of objectivity.
From Here I part ways with Rovelli:
Rovelli and I are in full agreement when it comes to our view of the
nature of physical reality: there is no absolute world of tables and
chairs with defined mass, position, momentum, etc., out there, but
instead an entirely relational world.
In my view, if the physical world has no standalone reality and is
entirely relational, then there necessarily is a deeper, by definition
non-physical but absolute (in the sense of not being relative) layer
of reality that grounds the physical world, and of which the physical
world is but a measurement image akin to a set of dials. I've known
for a while now that Rovelli isn't comfortable with this conclusion of
Kastrup thinks that at the bottom there is a universal consciousness that works through quantum excitations (or the "will", in the words of Schopenhauer). Here, There are some obvious parallels to the idea of Brahman in Advaita Vedanta philosophy. Especially that Kastrup's argument relies on the fact that conscious agents dissociate from the whole like in multiple-personality disorder, which is akin to the Eastern doctrine of dualism. The "cure" is to be eventually reunited with the whole.
Of course, the drawbacks and the criticism are clear. This is not actually a scientific theory (not even a hypothesis), but well-argued metaphysical speculation. If you play this game, then you play at your own risk. Ultimately, arguments both ways are "nullified" because they are not really testable, nor falsifiable.
But if you insist, then see the arguments of the opposite camp. Kastrup's arch-enemy is Daniel Dennett who holds the opposite claim; all is matter, and consciousness is a kind of illusion. If you want to find good arguments for it, read "Consciousness Explained*".
*- ... away