endowed by their Creator with certain unalienable Rights [...] rights are inherent,
Only if you believe in a creator that determined these right, which is not rooted in fact, but solely belief.
Personally, I do not believe a particular ethics exist as an absolute/scientific truth. It is just that some amount cooperation is generally better for everyone and virtually all humans want to avoid pain and seek happiness.
Even though I was a convinced utilitarianist when I was young, I think Kant's categorical imperatives are more powerful now: you should act only according to principles you would want everyone to adopt as a universal law. Or Rawls' original position [1].
Even though this might sound like an off-topic philosophical debate, I think it is very relevant to democracy. Purely egoism-based democracy would trample on the rights of minorities, etc. But in a democracy based on these principles, the majority would vote to project minorities, etc.
I am not sure how you would modify democracy to align with this. I think it is for a large part of education. E.g. if everyone thinks every choice is a zero-sum game (my loss is another's win and vise versa), democracy will go in a very dark direction.