What is a "magic ability" for the purpose of antimagic field, an 8th-level rare spell? No class feature or class feat ever lists down whether or not it is a magic ability.
Is a rogue's 18th-level Implausible Infiltration (which, by the way, is actually a decent example of the kind of noncombat abilities martials should be receiving) considered a "magic ability"? What of a barbarian's 6th-level Animal Skin, which has the Primal keyword? Or a paladin's 9th-level Holy Smite?
Also, I do not think an antimagic field should take away unarmed characters' handwraps' expert, master, or legendary quality. That is just mean to them for no reason.