Rudolf Steiner introduced what he called "spiritual science" from the established German term Geisteswissenschaften a term that comes from an idealist's interpretation of the Humanities, the realm of the development of the human soul including the study of philosophy, theology, poetry, literature, and art. Steiner's usage is both distinct, yet not completely unrelated. It is his interest in developing the capacities of the human soul so that it is more receptive to the divine world.
Steiner, no matter how unusual some of his ideals may seem, never advocated a bullheaded opposition to scientific development. He only suggested opposing the isolated elements in science that are directly antithetical to life itself. Other than that, we were to use technology rightly in service of others and the Earth. Biodynamics does not replace science, nor does it replace common sense farming. It is merely added.
When Steiner talks about "spiritualizing" the sciences, he means bringing a spiritual gaze to the research performed using the scientific method. He is not proposing the method itself change, but the gaze of intuition must always be brought to bear on the data science produces, or we would make very few connections at all. Steiner does not intend to reduce spiritual life to a the scientific method, but urges us to bring spiritual values into our scientific efforts. Which is to say, we must remember our humanity when using science. Science for the sake of science is dangerous when it forgets to be in service of humanity.
Steiner said that for every step of inner development we make, we should take three steps in developing the heart. I'd wager this applies to external sciences as well. In both cases, power is increased, and thus compassion must always be increased at a threefold greater rate.