What your doing isn't a clean install it just a reinstall of firefox. Clean means you delete the firefox app/data folder that will clear out everything and profile. That's the only way for no previous firefox to mess up install otherwise a complete reinstall of O/S that wipes clean everything to make a clean/fresh install of everything.

I'm trying to do a clean install of firefox, but every time I uninstall the program, when I reinstall it, it restores all my previous cookies and setting and that is exactly what I need to not happen, and I am not given an option to prevent it.

The Firefox settings are not in the Firefox folder but in a separate place as to why you can still have your stuff like bookmarks, passwords, extensions cookies, history etc still there.

https://support.mozilla.org/en-US/kb/uninstall-firefox-from-your-computer https://support.mozilla.org/en-US/kb/profiles-where-firefox-stores-user-data https://support.mozilla.org/en-US/kb/back-and-restore-information-firefox-profiles