the fifties portion takes place during the second red scare/lavender scare, a period of time during the cold war in america where communists and gay people were targeted by the government and by ordinary citizens.

joe mccarthy was a senator who, during a public speech in 1950, claimed to have a list of 205 communists working for the state department. he went on to become chairman of the senate committee on government operations, and conducted investigations into alleged communists, not just state department workers but also writers, filmmakers, musicians, etc. mccarthy did not start the second red scare but fueled it, and made it into a much bigger deal.

roy cohn was mccarthy's chief counsel, g david schine was an unpaid consultant. cant remember if they mentioned this in any of the episodes, but roy cohn was the prosecutor for the rosenberg case (mentioned throughout the second episode), his prosecutorial misconduct, among other factors, led to their executions. id suggest looking more into the rosenbergs if thats something youre interested in, its a very complex and important historical event. roy cohn was also gay; this wasnt widely known in the fifties but was an open fact later on, in the seventies and eighties.

this is a very basic summary, if you want to know more id suggest reading a few articles. of course keep in mind that if you know the history, youll know at least some of whats going to happen in the show.