The answer, as in all complicated questions, is yes and no. The way the United States acted under senator McCarthy was a dark period of the country. There was little concern for due process and evidence. Allegations were enough and many people were put on black lists. To be sure this was in the heyday in the 50s, but some of it was still around in the 60s. In this sense, the fear of communism was overblown.
On the other hand, the fear of a communist takeover was real. All you need to do is think of the events in 1962. The United States failed in their attempt to topple the regime in Cuba. At that time, there were some photos taken of Russian missiles being put together in Cuba, which caused immense fears due to the close proximity of Cuba to the United State. In time, we would call this the Cuban Missile Crisis. These events nearly led to war. Hence, fears were valid.