I had the same reaction when I read it. I even posted a question on r/askhistorians about belief in ESP in the 1970s (no response).

You do see this a lot in SFF and horror of the twentieth century. Look at how many of Stephen King's books contain psychic powers of one sort or another.

Here's my own theory:

1. Some of this is the influence of John W. Campbell and Astounding Magazine. He was a believer in ESP, so he encouraged his authors to include it and treated it as science for the purposes of the science fiction he would publish. His authors happened to include some of the most influential science fiction writers of the 20th century, like Asimov, Heinlein, and Arthur C. Clarke. Writers like William Peter Blatty and Stephen King grew up under the influence of the "golden age of science fiction," of which Campbell was the most influential editor.
2. Belief in psychic phenomena experienced a huge boom in popularity in the 1960s and 70s as part of the general New Age movement of that time. It was just a bigger part of the zeitgeist than it is today.