The phrasal adjective meaning strict in behavior or morality is strait-laced, not straight-laced. Strait here bears a mostly archaic definition that survives primarily in this phrasal verb—namely, narrow, constricted, or fitting tightly. It’s possible to imagine where straight-laced might make sense (for example, in contrasting straight laces with curved ones), but such instances don’t come up often.
Examples
This movie is about a bunch of strait-laced guys who hit Vegas for a bachelor party. [Screen Junkies]
Janzen’s parents are a great advert for strait-laced Christianity. [The Guardian]