I suspect the straight-edge "X" comes from the marks the ID checkers at the bars where DC bands played were placing on the hands of 18-21 year olds (or less than 21 year olds in general) as a notation to the bartender(s) not to serve them.

I'll also note that (at least later versions of) the liner notes for the song Straight Edge added "I" in brackets to the three claims in the chorus.

-brendan