Yes, reality is objective, but it’s not classical. Unitary-only quantum theory suggests the superposition principle never breaks down (cf. Wigner's friend); and experimental evidence confirms quantum theory is correct. In some branches of the universal wavefunction, the March 2019 MIT Technology Review says that “A quantum experiment suggests there’s no such thing as objective reality”. Such headlines are sensationalist. Physics has not gone post-modernist. The existence of ill-named observers who make inconsistent observations would threaten objective reality only if perceptual direct realism were true. None of us can directly access extra-cranial reality. Our minds run data-driven world-simulations that track different measurement outcomes in different quasi-classical Everett branches, all of which are tenselessly real and never cease to interfere.

In fairness, some physicists disagree with this perspective. For two nice non-technical overviews of the contested foundations of quantum physics, see Philip Ball (Beyond Weird (2018)), who is more sympathetic to Copenhagen-style positivism, and Adam Becker (What Is Real? (2018)):
‘Beyond Weird’ and ‘What Is Real?’ try to make sense of quantum weirdness.