They are wrong. Those dictionaries simply cave in to the morons after a couple of decades. They are useless.
“Strait” means tight. It is nonsensical to say “straight-laced.” Laces aren’t straight! They go back and forth!
They are RIGHT. ‘Straight’ can mean to be within societal norms. A person who is Straight-Laced is laced so tight they never deviate from societal norms, ever. So, I feel ‘Straitlaced’ is RONG. RONG. RONG!!!