Straight was a word with several different connotations.
But in at least 1967, and in at least San Francisco, it meant roughly the same thing as L7 or square. Jack Stimson sometimes would append the word edge, as when he looked at a picture of Denny Glass and called him a "straight edge". In this sense, it meant people or things that were not connected to the counterculture movement. Jessica Willamy often called things opposed to her world view "straight", such as the "straight city", when referring to the part of San Francisco that was not the Haight, or the "straight press", when talking about newspapers other than the San Francisco Oracle. (PROSE: Wonderland)