There is no specific mention of the Communist Party in the law. It is still against the law today (AFAIK) to advocate the overthrow of the US Government by force. In many countries today, even what we consider to be advanced countries in the EU, specific named political parties are illegal per se, and my point is that this is not the case in the US.
I can only speak for Germany where the specific parties forbidden are the NSDAP, the attempted rebrand SRD and the Communist Party. The NSDAP was forbidden by the Allied Council which included the United States. The latter two were banned because they were in breach of a German law (Art. 20 GG) perpetuating the republic, democracy and the social welfare state - a law which was formulated on experiences made in 1933 and encouraged by said Allied Council. The whole GG had to be approved by the Allied Powers as well. So they were essentially deemed "unconstitutional".
It's all well being against party bans until a country makes the experience of a fascist party being democratically elected into power and then abolishing democracy. Enacting laws which make a party illegal that has the abolishment of democracy in their agenda, even without explicitely calling for violence, makes a certain sense. Yes, you can always make the philosophical argument that any government can abuse this to just outlaw the competition, but at least in Germany, that has not proven to be the case in the last 60+ years. I don't think a whole lot of people would content that it was necessary for the fledgling democracy to outlaw the bureaucracy of it's predecessor dictatorship. And while the
Communist Party was banned, there are other communist parties in Germany. One is currently the third biggest political party and has participated in coalition governments of various federal states.
It's also easier to be laissez-faire about it in the United States, where an electoral system is in place that makes it nigh impossible for any party outside red and blue to be elected in the first place.
There are many boycotts today, by both sides of the political spectrum but especially conducted by the left
That's a nice display of selective perception.
If you believe it is OK to do boycott products
Depends what you mean by boycott. If individuals or groups choose not to frequent certain businesses, it's all well.
What I've always been appalled by is the (not exclusively, but frequently) American tradition of sign-wielding in front of somebody's home or business. Because that is in my humble opinion not boycotting, but Defamation. In the same vein do I find it ridiculous to eat there to support the notion of disadvantaging a minority.