I was previously using a different addon, Neat URL. I disabled that one so I could give ClearURLs a proper try. However, I realized that every time I restart Firefox, ClearURLs gets disabled, and Neat URL is re-enabled. Suspecting some sort of misbehavior from Neat URL, I fully removed Neat URL. However, even after that, ClearURLs is still showing as disabled in my addons list every time I restart Firefox. What's going on? I've never seen this behavior with any other addon.

EDIT: I figured out what was going on. Back when Mozilla had the certificate debacle that resulted in addons getting disabled en masse for everyone, I made my extensions.json file read-only as an attempt to keep my addons forcibly enabled. After the official fixes from Mozilla, I forgot to uncheck "read-only" from extensions.json. ClearURLs was the first new addon I've tried since that time. Anyway, when I tried to disable all my addons as a test, they came up as re-enabled when I restarted Firefox. That's when I finally suspected my extensions.json. So, I realized that was still read-only. Fixing that, now everything is working as expected. I'll update my ClearURLs rating to 5-stars.