Who makes that distinction?

Anyone versed in basic political theory.

An ideology and a political organization are obviously different. Just like republicanism and The Republican Party, democracy and The Democratic Party, socialism and The Socialist Party, etc.

destroying the state

That's technically sedition, so, yes, illegal.

Capitalism

Nowhere in U.S. jurisprudence is "capitalism" (verbatim) explicitly protected as an economic system. The 14th Amendment's Due Process Clause prevents the state from taking someone’s life, liberty, or property without a proper justification under the laws of the land. The Constitution protects individuals from the government. Freedom to contract is a principle that underpins the basis for a free-market economy.

After the Great Depression, the Court began to treat the freedom to contract as less than absolute, asserting that such freedom may be limited by the State’s interest to protect its citizens. Capitalism is a right guaranteed by the constitution but limited in scope to protect individuals against the dangers of laissez-faire capitalism.

class divides

There are no explicit laws in U.S. jurisprudence (that I know of or have turned up on brief internet searches) that enforce "class divides".

money

Be it resources, precious metals, or legal tender, money is protected by the 14th Amendment's Due Process Clause.

So we can conclude that the advocacy or practice of communism isn't itself illegal. Forcing people to practice it or overthrowing the government and dissolving The Bill of Rights in order to force people to practice most certainly is.

In my opinion, that's a good thing.