When I went through flying training in the early sixties, I was told that not lowering flaps in a turn started with the Wellington. It would seem that this aircraft tended towards asymmetrical flap-....like one might move but not both!
Thus it was thought that lowering during a turn might initially obscure a dangerous failure. Subsequent designs usually had both flap asymmetry detection and lock-outs should it start.
The same was said about never turning towards the dead engine but again, this was before the knowledge about safety speed and crit speed had been hard earned.
I have to say that since then I have raised and lowered flap (or called for the flaps to be raised or lowered) on many types without concern and even turned towards the dead engine when circumstances required.
...but then I read the bit about the Cessna flaps!