North Korea launches intercontinental ballistic missile to space, reaches record altitude

Any worse when when a nuclear armed government revolves exclusively around a single ideology?
Depends on the ideology, and how it is incorporated into the society. So, no definitive answer to your question.

It is also not clear to me whether Kim Jung Un could actually order a nuclear strike on another country, at least without being invaded to provoke it. The resulting nuclear counter attack would be the end of North Korea. So, would a person with the ability to actually "press the button" do so if ordered by Kim? Who knows?

In way of contrast, some theologies teach that the end of the world is the beginning of life in Paradise, or H e (double L), and that how you die determines which place you go for the rest of eternity. A small group of people who actually believe that could probably initiate a nuclear first strike, knowing that they are going to die, and believing that their deity will reward them for doing it.