There was a timeline split right after the 1950s which means no Vietnam War. There was no hippie movement and that also means there was no civil rights movement. At least not like what happened in our timeline. Everything stayed in the 1950s mindset right up till 2077.
I believe that there might have been a civil rights movement and "counter-culture movement". I'm not 100% sure about the civil rights movement occuring, since the lack of racism in the game from either pre-war or post war times doesn't necessarily indicate the movement occured (because that can likely be attributed to obvious factors not involved with creating the universe timeline).
In regards to the counterculture movement of the 1960s however, it appears that some form of it occured, as the people of megaton sometimes refer to the Church of Atom as "hippies" which would indicate that they have some understanding of that term and thus that the counterculture movement occured (that and the fact that the word exists at all).
The Vietnam War almost certainly did not occur, but it is not out of the question, since the War was brought about partly due to fears of the takeover of communism in east asia (which would fit the 1950s mindset). However given how you said that the War memorial is not there, its likely that JFK didn't bring the country to war (which some speculate would have been his position in real life had he survived).
As for the MLK memorial, it doesn't need to be put in because there are a many reasons why it might not be there. Even if the movement occured, its likely that MLK wasn't a major part of it at all in the alternate universe of Fallout.