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#JavaScript (ES6), 53 52 bytes
Saved 1 byte thanks to @tsh
Takes input as 3 distinct parameters: (Color, From, To).
(Color, From, To)
(C,F,T)=>T.replace(/\w/g,(x,i)=>C[F.search(x)-~i%2])
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#JavaScript (ES6), 5353 52 bytes
(C,F,T)=>T.replace(/\w./g,x=>C.substr(Fx,i)=>C[F.search(x),2)-~i%2])
Try it online!Try it online!
#JavaScript (ES6), 53 bytes
(C,F,T)=>T.replace(/\w./g,x=>C.substr(F.search(x),2))
