I assume the quest should be abandondable given it's a sidequest not a main scenario quest (the ability to repurchase AF armour at the Calamity Salvager is only unlocked after completing the quest) - have you opened your Journal and see if there is the 'Abandon' button in the bottom right of the quest description?

The only other alternative I can suggest (and this is an extreme option that's a last resort) is to buy the level skip for MRD/WAR from the Mogstation that will grant you the full set of AF gear automatically, setting the full quest line to complete (as well as automatically levelelling you up to level 80) However if you're enjoying levelling it and playing through it's storyline then it's not reccomended.