The reason I say our country encompasses elements of both is because at the local level pure democracy often exists as in when town councils post a referendum for the people to vote on. The majority will have their way and although every voter decision is subject to a judicial review if challenged, that is the case in a Constitutional as well as a Democratic Republic and even in a Democracy.
We have seen in other countries how the people have voted for something only to see a Judge overturn their vote because he feels differently
I get what you say about the Marxism but in reality what they espouse never has happened in the west to my knowledge.
I still maintain our government incorporates elements of both a Democratic and Constitutional Republic and there are other who agree. It is merely an opinion and we can agree to disagree.
States can do whatever they want. That was the plan to allow experimentation with States as long as they did not interfere with other States. The Federal govt is not in any way a Democracy and was intentionally set up to prevent such.
Our country Government is only Constitutional Republic - what you do locally with local issues is not within the realm of the Feds unless it runs afoul of an incorporated protection from the Bill of Rights.