Mentioning non-academic pre-PhD work on one’s website? Does mentioning non-academic pre-PhD work on one’s website help or hurt one on the academic job market? 

I’m a graduate student in political science approaching the end of my PhD and preparing to go on the job market next year. 

When I began my PhD program I created a website, and in the personal section I briefly describe my pre-PhD work, which includes working for some well-known political figures in well-known organizations. At that time, I felt like my prior work was a big part of my identity and therefore included it in my bio.

I know this may be minor point, and the quality of my academic publications and dissertation is much more important than a paragraph of my website bio, but I’m asking because this could make a marginal difference when I apply for jobs.

For example (not real): Before starting graduate school, I worked for Bill Clinton as international policy advisor from 2006 to 2008. From 2008 to 2011, I worked in the office of President Barack Obama as multilateral affairs advisor.
Your professional website should reflect your professional identity.  That obviously includes all of your scientific work, but may also include other aspects of your life that you choose to share broadly with colleagues.  For example, some people put bits of their hobbies or family life on their page; others (like myself) choose not to do so.

If your political involvement is something that you feel is relevant and that you want your possible future colleagues to be aware of, then by all means keep it on there.  If you feel it is likely to be distracting (e.g., you were campaign manager for a famously corrupt and now-indicted politician) then removing it might be better.