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.