If the right-wing supporters claim the left-wing equates to anarchism, whilst the left-wing...?

The US form of government if the Constitution is followed, could never lead to anarchism or fascism. The use of those terms by people is hyperbolic rhetoric. The "right-wing" and "left-wing" are for neither of those extremes. The differences are more about how and what control or responsibilities the federal government should have. Myself, I think government should be more limited and more focused on what powers they were allotted in the Constitution. People are the only holders of rights government only has the privilege of powers given to them by the agreement of the people. If the Constitution is followed, government has no power to take rights belonging to the people away for any reason other than for a particular person that has harmed another or violated another's rights. I don't think that's a right or left position just a Constitutional one that preserves liberty for all people.