I’m embarrassed for you that you’d want to debate this with people without having ever opened a book on political philosophy.
Here's some more truth for you to search out from the encyclopedia britannica:
Republic, form of government in which a state is ruled by representatives of the citizen body. Modern republics are founded on the idea that sovereignty rests with the people, though who is included and excluded from the category of the people has varied across history. Because citizens do not govern the state themselves but through representatives, republics may be distinguished from direct democracy, though modern representative democracies are by and large republics. The term republic may also be applied to any form of government in which the head of state is not a hereditary monarch.
I would also think that we should keep in mind that Party politics (regardless of which one) are NOT protected by the Constitution.
Someone please find the citation in the USConstitution that “protects” any political “party” during a primary season. As a matter of fact, give me the citation that calls/protects what we now call a “primary election” at all.