Wait a second...
Wait a second...
The real question is how do you protect people from themselves?
Education.
In an education system people are taught to think, and given intellectual keys, and material for thought. The values imparted are the natural ones, consequential (e.g. "work, or no results") - not factioneries.
There is no rational process for deriving values and morality from first principles. Science is about what is, not about what should be. Democracy therefore can't be derived from facts of nature alone. You can only reason from true things to other true things, not from nothing to something. There is no reasoning your way from physics to how a state ought to be run.
Your mention of sharing the same ideas or not was already clear before, and it does not matter, because beliefs are lowly things hence not part of this game. You are talking about arbitrary ideas taken as "values" - no, those were not in topic.
You are clearly taking 'education' with a meaning that is completely different from the one intended.
Repeating: «In an education system people are taught to think, and given intellectual keys, and material for thought». The educated will assess, being enabled to an ability of properly assessing. This also means: there is no "doctrine", the educated has its own judgement. Whatever is doctrinal has no part in education, but for material for dissection.
And yes, there are «process[es] for [in some way] deriving values and morality from first principles». As explicitly mentioned before, students for example will be shown that results come from well spent effort: that "well spent effort" is a value. They may be brought to experience that persistence enables them towards results: that grit is a value. That such quality requires resisting cheap gratification: that control is a value. They will receive the information of ancient wisdom, from Gilgamesh on, through Aesop and on, and on, and on, and they will have the nourishment to form the basis of wisdom. It is very clear in some twisted behaviour that some people never met very basic ideas, that instead in some cultures correctly are told to children very early. You give people facts, they will learn from them - wisdom very much included.
(I will not discuss about Science for brevity, and I do not know why you would bring "Democracy" to the table.)
But anyway, the discussion over values was not original in the discussion, it was proposed. The original point was: people empowered to take decisions can make bad decisions, with catastrophic results. How do you protect people from people: you educate them, so that they can take better decisions through better intellectual qualities, hence better judgement.