Due process is the legal framework that is supposed to protect us from being snatched off the street.
It can mean a lot of things, but generally its supposed to be a process for determining if someone can be arrested, and to offer them an opportunity to mount a defense.
If they are allowed to make one exception, it all crumbles - they can just grab you on the thinnest of excuses. Wrong race, wrong language, wrong neighborhood. Or because an officer doesn't like the way you looked at them...