Communism, as an economic system, is not inherently at odds with representative democracy (and I don't know of anything that declares capitalism to be the official economic system of the US). Regardless of the stated aims of the Communist Manifesto, as a political party, it is theoretically possible for the communists to come to power in the US without "illegally overthrowing" of the government. That realization is probably why it was considered dangerous enough to be declared illegal per se.
The Red Scare stomped all over people's constitutional rights. It was trial by innuendo and guilt by association. If you were called to testify you were damned if you did or damned if you didn't. What it proved was how thin the paper is on which our rights are written when people are driven by unreasoned fear.