Having read comments from some Brits who wish to get rid of the monarchy in order to turn their country into a “democracy”, I despair. It is one thing that, in 2024, most folks are illiterate when it comes to science and technology but apparently, history and the social sciences are also badly neglected subjects.
My point, of course, is that these commenters confuse the form of government with the sources of power and the nature of the state.
A form of government may be a republic (res publica, i.e., governance in the name of the public) or a monarchy (monarkhia, rule of one), among other things.
However, both these forms of government can be autocratic (relying on the might of the state) vs. democratic (relying on the will of the people) insofar as the source of power is concerned.
And neither the form of government nor that source of power determine if the state will be liberal (that is, respecting basic rights and freedoms, such as freedom of conscience, freedom of enterprise, or the rule of law) or illiberal/authoritarian.

Midjourney’s response to the mostly Claude-written prompt, “Three regal anthropomorphic cats sitting on thrones, representing the orthogonal concepts of government. One cat wears a crown (monarchy vs republic), another holds a scepter and a ballot box (autocracy vs democracy), and the third balances scales of justice (liberal vs illiberal). The cats are arranged in a triangle formation against a backdrop of a stylized world map.”
To illustrate, let me offer a few examples. I live in Canada: a liberal, democratic constitutional monarchy. South of us is the United States: Also liberal and democratic, but a republic.
In contrast, the DPRK (North Korea) may serve as an example of a state that is an illiberal, undemocratic republic. Saudi Arabia is an illiberal, undemocratic monarchy.
Examples for other combinations are perhaps harder, but not impossible, to find. Orban’s Hungary, for instance, is rapidly converging on a state that is best described as illiberal, but democratic (the primary source of power is the people, not the might of the state) republic. I think some of the states in the Middle East (maybe Kuwait?) might qualify as relatively liberal, yet undemocratic monarchies.
These categories are not perfect of course, and do not cover all outliers, including theocracies, transitional governments or failed states. Still, I think it’s important to stress that the form of government, the source of power and the nature of the state are three fundamentally orthogonal concepts, and that all combinations are possible and do exist or have existed historically.
Understanding these distinctions is important. For instance, there are plenty of historical examples (e.g., the French Revolution devolving into the Reign of Terror, or the Russian revolution leading to the totalitarianism of the USSR) when the transition from monarchy to republic led to a significantly more autocratic regime. “Republic” is not a synonym for “democracy”.