XOR sort an array

Python 3, 75 73 bytes

lambda k,x:x.sort(key=lambda s:[ord(x)^ord(y)for x,y in zip(s,k*len(s))])

This sorts the list x in-place.

Thanks to @mercator for golfing off 2 bytes!

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Alternate version, 62 bytes

This takes input as byte strings, which may not be allowed.

lambda k,x:x.sort(key=lambda s:[*map(int.__xor__,s,k*len(s))])

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Jelly, 9 7 bytes

⁹ṁO^OµÞ

Thanks to @EriktheOutgolfer for a suggestion that helped saving 2 bytes!

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How it works

⁹ṁO^OµÞ  Dyadic link.
         Left argument: A (string array). Right argument: k (key string).

     µ   Combine the code to the left into a chain.
         Begin a new, monadic chain with argument A.
      Þ  Sort A, using the chain to the left as key.
         Since this chain is monadic, the key chain will be called monadically,
         once for each string s in A.
⁹            Set the return value to the right argument of the link (k).
 ṁ           Mold k like s, i.e., repeat its characters as many times as necessary
             to match the length of s.
  O          Ordinal; cast characters in the resulting string to their code points.
    O        Do the same for the chain's argument (s).
   ^         Perform bitwise XOR.

Haskell, 77 bytes

import Data.Bits
import Data.List
t=fromEnum
sortOn.zipWith((.t).xor.t).cycle

Too many imports.

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