Mentioning non-academic pre-PhD work on one’s website?
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.