President Reagan is the man who began the Presidential Return Salute.
Dwight D. Eisenhower
Civilians do not return a salute, they aren’t military. Even a President who served in any branch of the US military, serves as the civilian head of the Armed Forces as Commander-in-Chief. As an example, President Eisenhower never returned a salute while he was in office even though he was a General of the Army (5-star).
While the President is the only civilian who receives a direct salute (one-on-one), all civilians may receive an indirect salute (like in a cordon).
President Reagan, wanted to show his respect to those on Marine One, Air Force One, and at the White House. It wasn’t enough for him to just receive, he wanted to do something in return.
Each President since has continued the tradition to varying degrees (I do not think this is the place to get into the terrible salutes of each subsequent US head of state). I understand why President Reagan did it and that if any President after him would have discontinued the tradition, he would have been vilified most likely.
President Trump has extended the use of the salute to beyond just returning a direct salute from members of the military. He will render a hand salute for ceremonies at the Tomb of the Unknown Soldier, for example.