It's funny that you list Einstein as your example of someone who is "innocuous" — he would have vehemently disagreed! Einstein had very strong political opinions which he advocated very publicly on matters such as socialism, Civil Rights, world government, and nuclear weapons. He was for his time pretty far left, though not a Communist. The FBI was investigating him because he was an extremely prominent person who was advocating what they considered to be subversive beliefs, and he had associates who had connections with organizations like the Community Party USA. He was also a naturalized citizen which meant they could, if they built up enough of a case, get him stripped of his citizenship and deported — something they were trying to do before he died. The apolitical, science-grandpa Einstein that people think about today is a completely white-washed myth, and certainly does not reflect how Einstein saw himself or acted. He was in many ways a political radical, and his widespread fame and respect for his scientific intelligence made him dangerous in the views of Hoover.

Similarly, Hoover clearly thought the Civil Rights movement was just Communism by another name. In such a situation he had no problem using whatever tools he thought were at his disposal, including quite shameful and ridiculous ones.

There is more that can be said about this, but these two things about your question jumped out at me as reflecting something of a misunderstanding about how the FBI viewed these two topics. There may be examples of the FBI doing investigations that had no substantive likelihood of uncovering "subversion" by their definition, but these two are definitely not that.