Jelly, 37 bytes

“ETIANMSURWDKGOHVFaLbPJBXCYZQ”iⱮḃ2FŒḂ

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Jelly, 28 bytes

ØAŻŻ“¡9o|çṫ¡X1ỴỌġQ’œ?iⱮḃ2FŒḂ

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ØA                             The uppercase alphabet.
  ŻŻ                           Prepend two zeroes.
    “¡9o|çṫ¡X1ỴỌġQ’œ?          Get the 73540211105102870315464559332nd permutation.
                                  (= “ETIANMSURWDKGOHVF0L0PJBXCYZQ”)
                     iⱮ        Find indices of input letters in this list.
                       ḃ2      Bijective base 2: map [1,2,3,4,5…] to
                                 [1], [2], [1,1], [1,2], [2,1], …
                         F     Flatten.
                          ŒḂ   Is palindrome?

I wrote this answer looking at one of these (read the rows from right-to-left, and you get my magic string!):