Yes.
Also, there seems to be things that are magical in origin, but that are nonmagical now.
When trying to get a sense of these (recent) considerations about what is or isnt magic, I found dragonbreath to be illustrative.
Presumably, the dragon "evolved" into a firebreather, by means of magic, whether shapeshifting or elemental, or whatever. But now, both its ability to produce fire and the fire itself is effectively nonmagic. Probably the same goes for dragon flight. It is possible to use reallife science (biology, aerodynamics, etcetera) to explain why a gigantic dragon can fly (like bladders with buoyant gas). But D&D can handwaive it, and say, sure it came from magic, but is effectively nonmagical in itself. A dragon can continue to firebreathe and fly while in antimagic.
If I recall correctly some undead frightening effects, seem quasimagic, but are effectively nonmagical.
There are other blurry lines. The psionic power source can cast spells. The ability of a mind to do these things is natural and innate, but the spells that manifest are magical.
Anyway, I am still trying to get a feel for what is and isnt magic.
In the case of the Druid, the class will continue remain proficient with nonmetal armor, no matter where this knowledge came from.