Seems pretty straightforward. You cast the spell while you were allowed to do so, and since it doesn't require concentration, it keeps functioning while you rage. You have a specific rule that says your version of magic weapon doesn't require concentration, so it doesn't end because of an effect that solely affects spells that do require concentration.

This version of Magic Weapon keeps functioning while you rage

Seems pretty straightforward. You cast the spell while you were allowed to do so, and since it doesn't require concentration, it keeps functioning while you rage. You have a specific rule that says your version of magic weapon doesn't require concentration, so it doesn't end because of an effect that solely affects spells that do require concentration.