Where science is only a tool to work with what we perceive to be the physical universe (and should be seen as such), the general population has now been deeply conditioned to confound science with philosophy.
It is the /misuse/ of science /as/ philosophy that is the problem: where science and its fundamental first principles (and the "physical universe" that it examines) is taken for ultimate philosophical reality, rather than as emerging perceptual manifestations of something more primary (possibly consciousness). The issues arise from the philosophical adoption of the classical view of science (not even the modern one) that these atoms and molecules and particles and so forth and so on are the "things" that "make up" a "physical universe" in which consciousness arises from a physically-mattered brain. It is a redundantly reductivist worldview, and a highly dogmatic one at that—a fact which you can easily confirm when speaking with pretty much anyone in the modern West about alternative metaphysical theories that will be sooner shot down as being new-agey or religious or whatever else than seriously considered as potential metaphysical realities. We talk so much of the cultural value of open-mindedness, yet any non-materialist worldview is so heavily stigmatised that anyone found seriously to entertain them are often seen as being on par with the likes of religious nutjobs or woo-woo new age idiots.
While science as a discipline /itself/ does not make such metaphysical claims, it is the dogmatic adoption of science as the ultimate truth by the populace (and scientists such as the ones referred to in the video), and thereby the dogmatic rejection of any alternative metaphysical worldviews (such as that mind is primary, not tertiary), that Sheldrake denounces for its role of limiting our potentialities through hubris and close-mindedness.
Science is useful for what it is, but if we believe ourselves to have figured out the fundamental nature of the universe (mainly the assumption that it is made up of physical particles in which consciousness just happens to be embedded), just because it follows certain perceptual patterns that we perceive through our limited rationalities and sober minds, we will only be fooling ourselves into hindering meaningful progress for our collective consciousness in an otherwise infinite and incomprehensible universe.