Acting on behalf of adversarial governments is fine too if you register with the government. In the case linked above they didn't do that and conspired to keep the fact they took orders from Moscow hidden.
I think we would all agree on that, but don't you see a risk that this labeling could be abused pretty easily to punish dissidents or any other enemy of powerful people?
Is someone charged with drunk driving just "labeling"? What about manslaughter? First degree murder? Treason?
Someone being charged with a crime is a completely different thing to someone "being labeled" and trying to downplay the severity of the former to try and extend it to this hypothetical is telling.
When the West does it, it's called NGOs. When the East does it, it's called malign influence. Maybe it's time the West retire the free word from its world. It's two worlds at odds. And none of them is free (though in one you do definitively have a bit more rights and a semi-functional legal system).
The Espionage Act has been on the books for a century now and it was definitely used to punish dissidents. In some sense nothing new. But don’t be naive. There are plenty of countries waging various forms of attack against America at all times and there should be laws to thwart these attacks. The implementation and enforcement is key. Simply relying on abstract principles is the core danger of such a law, hence the need for a court that is itself accountable to the electorate. Either way the risks are abstract. The implementation is the key.
To confuse matters, many of these attacks aren't so much against America, as against the concept of liberal democracy.
To uphold liberal democratic values is to support the free speech that makes these attacks possible. The old 20th century style of propaganda was mostly ineffectual. The modern tactic of flooding public discourse with bullshit is much more effective. At some point people concede that maybe the shills and useful idiots working for the dictators do raise some valid points, so who knows what to believe.