The Constitution REQUIRES states to have Republican form of government, not a democracy.
Article IV, Section 4. The United States shall guarantee to every state in this union a republican form of government, and shall protect each of them against invasion; and on application of the legislature, or of the executive (when the legislature cannot be convened) against domestic violence.
We are NOT a democracy, either in whole or in part.
But we are being "invaded" -- more general government irresponsibility. But Hope and Change are coming -- DJT.
While the federal govt is a republic, I have not considered whether individual states are required, as you state, or just guaranteed the freedom to choose. I am not sure I read “required” and “guaranteed” as the same thing. It seems like individuals in states would certainly want that. For example, it does not seem right that the city of Las Vegas basically dictates how the rest of the state must live since it has a higher population than all of the remainder of Nevada. This is where ballot initiatives can become a two edged sword.