2021-09-28T02:41:03Z

The Barbarian 1st level ability Rage states:

If you are able to cast spells, you can’t cast them or concentrate on them while raging.

And the Variant Human: Mark of Making innate ability Spellsmith states:

You know the mending cantrip. You can also cast the magic weapon spell with this trait. When you do so, the spell lasts for 1 hour and doesn’t require concentration. Once you cast the spell with this trait, you can’t do so again until you finish a long rest. Intelligence is your spellcasting ability for these spells.

If I cast magic weapon first with Spellsmith, and then Rage, will it cancel magic weapon even though I don't have to concentrate on it?

2021-09-28T02:45:37Z

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.