It seems to me that we must make a distinction between what is "objective" and what is "measurable" in discussing the question of physical reality, according to quantum mechanics. The state-vector of a system is, indeed, not measurable , in the sense that one cannot ascertain, by experiments performed on the system, precisely (up to proportionality) what the state is; but the state-vector does seem to be (again up to proportionality) a completely objective property of the system, being completely characterized by the results it must give to experiments that one might perform.

But I think it is a serious issue to wonder about the other platonic absolutes of say beauty and morality.

If you didn’t have any conscious beings in the world, there really wouldn’t be morality but with consciousness that you have it.

No doubt there are some who, when confronted with a line of mathematical symbols, however simply presented, can only see the face of a stern parent or teacher who tried to force into them a non-comprehending parrot-like apparent competence--a duty and a duty alone--and no hint of magic or beauty of the subject might be allowed to come through.

As you say, the way string theory requires all these extra dimensions and this comes from certain consistency requirements about how string should behave and so on.

our present picture of physical reality, particularly in relation to the nature of time, is due for a grand shake up

Understanding is, after all, what science is all about — and science is a great deal more than mindless computation.