The idea that "nothing is objectively real prior to measurement" is a peculiar philosophical mishmash, kept in currency by the conjunction of two things: (1) the difficulty of producing an objective theory, without a special status for "measurements" or "observers", that reduces to quantum mechanics; (2) a multitude of nonquantitative philosophical ideas, motivated by the various ways in which our experience of reality is less than certain or complete, which seek to dilute or negate the idea of objective reality.
Quantum mechanics is an incomplete description of reality. This may be seen simply by noting that the theory in itself does not specify which observables take values - it is up to the user of the formalism to say which observables they care about on any given occasion. (I am here assuming that observables, not wavefunctions, are the "elements of reality".)
I have the impression that in the late 1980s, Murray Gell-Mann was hoping that a special maximal set of observables might be defined in the framework of consistent histories, which would thereby supply a natural answer to the question, "which observables, out of all the formal possibilities, are the ones that take values in the real world?" These special observables would then be the "beables" (John Bell's term), the objectively existing elements of reality that formed the ultimate grounding of physical ontology, beyond all considerations of observers and measurements. But investigators found a vast number of consistent quasiclassical possibilities, so interest in solving the ontological problems of quantum mechanics via consistent histories subsided.
Or at least, that is my speculation about what happened; someone should ask those who were on the scene, like Gell-Mann and Hartle, whether it has any truth. I emphasize this approach to restoring objectivity to physics because it is a fairly simple way to do so. It immediately raises further questions - e.g. why one set of observables rather than another - but it at least demonstrates that there is no need to be "anti-realist".
So far as I can see, the claim that "reality is subjective" - defended many times on his blog by this site's #1 contributor - does not say anything substantive about reality. Indeed, it is a zenlike, self-contradictory denial that there is anything objective to say about reality. I presume it has the psychological function of simultaneously catering to a physicist's natural intellectual need to have some conception of reality, while also providing a "reason" (or an excuse) to regard the framework of quantum mechanics as final.
Meanwhile, our #2 contributor doesn't say that reality is subjective; instead he espouses logical positivism, and seeks to dismiss questions about ontology, reality, existence, etc, as meaningless. This seems to be nothing but an overkill application of a valid epistemic principle, which is that if you're going to believe something, you should have evidence. The demand that theories should have observable, calculable consequences is a force for good, but once again, the historically unique situation regarding quantum mechanics - in which an inherently incomplete formalism remains our best description of physics for many decades - can lead a person astray from simple positivist caution to anti-realist zeal.
And those are the views of two quite good physicists, who cared enough about the question of "reality" to at least develop an opinion on how to think about it (however misguided that opinion may be). For other physicists, who don't hit upon a personally favored form of realism (whether it is Everett's multiverse, or 't Hooft's holographic determinism, or some other picture that restores objectivity), there may be pragmatism, private confusion, even a type of mysticism about the role of consciousness in reality.
Or there may be the peculiar type of "materialist idealism" described in this post, where the experimentalist's concept of "measurement" has the reality-creating role ascribed to "thought" or "mind" in traditional metaphysical idealism. Perhaps John Wheeler was the best-known occasional advocate of such views... My position is that quantum mechanics is incomplete, and the task, for those who accept it, is to produce a physics and a physical ontology which restores objectivity to the picture of reality. It's that simple, and that difficult. But some people will never be convinced of the viability of that course, until the task has actually been carried out.