I've moved from environmental biology to biomedical biology in my career. Certainly biomedical types don't care much about classification. But that's because they traditionally only deal with humans, rats, monkeys and mice. But classification really matters once you get beyond that. Hell, biomedical science is having a crash course in classification due to the current interest in the microbiome. It really matters if a bacterium is a Firmicute or a Bacteroidetes.