If you had actually read the Wikipedia article:
In 1973, a federal district court in Arizona decided that the act was unconstitutional, and Arizona could not keep the party off the ballot in the 1972 general election (Blawis v. Bolin). In 1961, the Supreme Court of the United States ruled that the act did not bar the party from participating in New York's unemployment insurance system (Communist Party v. Catherwood).
So yes, the law passed during the the McCarthy era ... and was afterwards declared unconstitutional.
The Communist Party USA is still around and even have a website.
One: you can be sued for anything regardless of if it's true or not. Someone could find some sleazebag lawyer and sue you for drowning hundreds of puppies while laughing about it -- does that make you a puppy killer?
Two: We have presidents that we know directly ordered genocides of native people ... yet weren't sued for it.