*'Space' has no objective existence in science as we know it, it is merely the emptiness between particles in a FLRW universe.*
I think Chronos is right from a GR perspective. The catch is we don't know for sure that GR is a correct picture of Nature in every regard. But in many contexts we tend to assume it is.
In the world as described by GR, points in space have no physical existence, but geometry does. GR is about the evolution of geometry as it interacts with matter.
Geometry does not require a material space substance----it can simply be about the geometric relations among events, about the geometric measurements we make (area, angle, volume etc.) involving actual material, about the other fields that live in a given geometry. It means something operational and definite without being a substance.
I think that is the GR view of it. Someone may want to correct me on this---what I said may be wrong or incomplete.
The catch is we aren't sure if GR is the whole story and if it is going to be replaced what the main features of the replacement are.
As I see it, standard matter physics MIGHT fit nicely into GR. It is about matter fields. Why couldn't the matter fields live happily in GR geometry? It hasn't been like that. Quantum field theory is usually done in a fixed geometry, not a dynamically changing expanding contracting etc geometry. But maybe the theorists can work that out. Or they can first quantize the GR geometry and then get matter fields to live in it.
Or both have to change----both matter physics and geometry physics have to change a little in order to be compatible.
You could say that is what some of the conferences have been about. I could have been talking about the June 2011 one in Zurich called "Quantum theory and gravitation." It brought together people from quite a number of research lines all having to do, one way or another, with this problem.