Clarification op, are you talking about the phenomenon we describe as being transgender or about individuals specifically called transgendered?

Check out Stonewall by Duberman. It's a little later than the 1950s, but It recounts the history of the Stonewall riots in New York, and the police raids of bars leading up to the riots. In the raids the police didn't discern much between being homosexual and transgendered. Having male anatomy and wearing a dress was categorized as the same type of deviant behavior as a man trying to have sex with a man. Lesbians and trans men could be arrested if they weren't wearing three articles of feminine clothing. During raids, biological sex would be verified by a female officer stationed in the restroom.

When the riots occurred, Duberman notes how witnesses characterize the drag queens as being the most outspoken protestors. This is where it gets difficult to accurately describe people. One person an observer describes as a drag queen in the 1960s might identify as a trans woman today. Or they may still identify as a drag queen. The perceptions of the time even among gay and lesbian people often failed to cover the distinction.