IMO, it was just Nixon's natural paranoia, and possibly furthered by his work for McCarthy, who in hindsight was remarkably "right" when the various KGB files were made public after the collapse of the Soviet Union.
Although it's still obviously arguable that those people could/should be able to maintain any beliefs, or personal contacts they wished in a "free society", however wrong they may have been to do so.
And honestly, coming back to today, it's Nixon's fate that might be what Obama is being spared if/when he loses this Tuesday. Fast and Furious, Bengazi, even his fraudulent foreign student status in college, and more... could all come to end his presidency in a second term, and harm the Democrats how Nixon did for the Republicans political fortunes for almost a decade.