It may not have been intentional by Clooney, but this movie came out around the time that conservative writers Ann Coulter and M. Stanton Evans published books attempting to rehabilitate McCarthy. In that context, the movie's a useful reminder of why McCarthy has such a negative reputation.
Periphery Demographic: Although the film does not protect the Communists, but only criticizes the paranoid fears about them, it was very popular among the American left, as it was perceived as Take That! for "government persecution". This also makes it attractive to modern Russians, who interpret anti-Russian sanctions and accusations against "Russian hackers and trolls" as "a new McCarthyism of the 21st century."
The Roosevelt-Truman administrations did have Communist sympathizers in them. However, that doesn't change the fact that few of McCarthy's claims were substantiated in the hearings. So more like "strawman's political maneuvering happened to align with reality." In fact, McCarthy admitted that the "list" he waved around at one speech was a mundane to-do chores list.
The point is that only one of the people McCarthy accused, Mary Jane Keeney, was actually anything close to guilty. Even then, McCarthy accused her of being a Communist party member, which distracted from the fact that she was actually a GRU spy and suggests that any attempts to claim that McCarthy "was right" suffer from the Texas Sharpshooter Fallacy: a man shoots wildly into the side of a barn, draws a target around the bulletholes, and then says "look at my deadly aim!"
In-Universe, Bill Paley notes that even Murrow was worried about looking like a Communist sympathizer by remaining silent about Alger Hiss. Murrow has no response to this. Instead, his defense is that at some point, a line has to be drawn.
Values Resonance: Although Mc Carthy's reputation was irreparably destroyed in society and he himself remained in the past, the message of the film about public paranoia and witch-hunting is all relevant in modern society, when intimidation and persecution is still a popular means of fighting dissenters.