That fundamental principle of democracy also demands that minorities still have their rights protected.

It depends on the democracy. Ancient Athens had democracy, yet women had basically no rights and slaves were a thing. In Sparta, which had 2 kings, greatly opposed democracy and a militaristic society(with abhorrent generational slavery), women had a lot more rights, were getting educated, etc. From Plutarch "quoting" Gorgo(Queen of Sparta, wife of Leonidas)

"Why are you Spartan women the only ones who can rule men?"
"Because we are also the only ones who give birth to men."

https://en.wikipedia.org/wiki/Women_in_ancient_Sparta

"Spartan women were famous in ancient Greece for having more freedom than women elsewhere in the Greek world. To contemporaries outside of Sparta, Spartan women had a reputation for promiscuity and controlling their husbands. Unlike their Athenian counterparts, Spartan women could legally own and inherit property and they were usually better educated."

Etymologically and historically, democracy just means that the people(majority) hold the power. The association of democracy with human rights, is a somewhat modern interpretation. If the people of Turkey or Egypt want their country to be an islamic country shouldnt they have that right?

I think it is complicated. And becomes even more complicated when you dont have freedom of movement between most countries(so people are basically doomed to exist where they are born). But i think preferring the military overthrow of a democratically elected government just because it doesnt align with your moral values, sets a very dangerous precedent that threatens the very core of democracy.

If Trump was elected, would you be in favor of a military intervention because he doesnt align with your moral values? Because this is exactly what many Trump fans were asking, after Trump lost the election. And once you start using military force to overthrow the elections, democracy is done.

force it on anyone else

We are forcing tons of things on people in democratic countries. Child education for example. While in the US, you can home "educate" your child, in most countries your child is required by law to attend a school. Raw milk is illegal in most countries. You are forced to pay health insurance(in countries other than the US). You are forced to wear clothes. You are forced to pay for state tv(except in the US) even if you never watch it.

Personal liberty is restricted. And you could argue that it is "for the greater good" but you could also use the same excuse for an islamic state that restricts homosexuality.