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Mustrum_Ridcully
I think it depends on what you consider magical fire to be. If it's the summoning of raw fire straight from the elemental plane of fire shaped into an explosive force, then the elemental ought to be immune. If it's the extraction of the natural fire that exists in your material component (Greek-style elements here) into an explosive force then, yes, I like your approach that you could 'extract' some of that fire from the elemental itself.
I kind of prefer the idea that feeding a fire elemental lots of fire spells makes it stronger, but that a spell probably exists to control fire elementals, which a fire mage would be better at casting. Maybe they need to define their (meta)physics a little in the DMG to explain some of these decisions.