Does becoming good at scientific research force one to become one dimensional? I'm an individual interested in multiple academic disciplines such as neuroscience, biological engineering, computer science, history, anthropology, psychology, political theory ... to name just a few. Currently, I have a normal (40 hours/week) engineering job that leaves me enough free time to follow these topics to a moderately satisfying degree. 

However, primarily due to intellectual curiosity, I'm considering doing a PhD (in Europe) and would ideally want to move to research later (discipline: something along the lines of genetic engineering, computational biology or cognitive neuroscience - not sure yet, but my background is in computer science). Given the highly specialized nature of modern scientific research that seems to demand intense working hours, one concern that I have is the fear of becoming highly one dimensional: completely failing to follow progress in other fields and in society as a whole, with publish or perish environment creating an inescapable feedback loop, where one cannot afford to read articles and books on topics not related to work, or follow public debates; yet alone write a blog about e.g. social issues.

I realize there are academics out there who seem to be prolific across multiple disciplines (e.g. Chomsky, Pinker ...), but the question still stands: in a modern research environment, can one satisfy multiple intellectual interests that transcend immediate work requirements, or has the game become too competitive and focused for that? What are the main variables?
You can do it, but you might not be a professor. I have a PhD in Aerospace Engineering, and I work in CFD, HPC clusters, and BigData/analytics when I do research. My primary job is running the HPC department at a large-ish computing center. If I were a professor, I doubt I could pull this off. My research output is much smaller that professors my age, but I still have a pretty satisfying career. 

You best chance for doing lots of different kinds of research is to find a center who appreciates you for your broad interests and to help it grow its mission while pursuing your more esoteric interests when you can.