Maximum Hamming distance among a list of padded strings
Jelly, 20 bytes

Not really happy with it. Should be golfable, even to ~15 bytes perhaps.

LÞŒcµṁ/sḢL$ŒsÐeFn)§Ṁ


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Explanation


LÞŒcµṁ/sḢL$ŒsÐeFn)§Ṁ    Full program or monadic link. N = input.                     | Example: ["abc12D5", "abC34d3", "ABC14dabc23DAbC89d"]
LÞ                      Sort N by length.                                            | [['a', 'b', 'c', '1', '2', 'D', '5'], ['a', 'b', 'C', '3', '4', 'd', '3'], ['A', 'B', 'C', '1', '4', 'd', 'a', 'b', 'c', '2', '3', 'D', 'A', 'b', 'C', '8', '9', 'd']] (in Jelly, strings are list of characters)
  Œc                    Unordered pairs: [x, y] for all distinct x, y in N.          | [[['a', 'b', 'c', '1', '2', 'D', '5'], ['a', 'b', 'C', '3', '4', 'd', '3']], [['a', 'b', 'c', '1', '2', 'D', '5'], ['A', 'B', 'C', '1', '4', 'd', 'a', 'b', 'c', '2', '3', 'D', 'A', 'b', 'C', '8', '9', 'd']], [['a', 'b', 'C', '3', '4', 'd', '3'], ['A', 'B', 'C', '1', '4', 'd', 'a', 'b', 'c', '2', '3', 'D', 'A', 'b', 'C', '8', '9', 'd']]]
                        Here, by distinct, I mean at different positions.            |
    µ            )      Map with a monadic link.                                     |
     ṁ/                 Mold x like y. That is, cycle x until it reaches length y.   | [['a', 'b', 'c', '1', '2', 'D', '5'], ['a', 'b', 'c', '1', '2', 'D', '5', 'a', 'b', 'c', '1', '2', 'D', '5', 'a', 'b', 'c', '1'], ['a', 'b', 'C', '3', '4', 'd', '3', 'a', 'b', 'C', '3', '4', 'd', '3', 'a', 'b', 'C', '3']]
       sḢL$             Split into chunks of x's length.                             | [[['a', 'b', 'c', '1', '2', 'D', '5']], [['a', 'b', 'c', '1', '2', 'D', '5'], ['a', 'b', 'c', '1', '2', 'D', '5'], ['a', 'b', 'c', '1']], [['a', 'b', 'C', '3', '4', 'd', '3'], ['a', 'b', 'C', '3', '4', 'd', '3'], ['a', 'b', 'C', '3']]]
           ŒsÐe         Swap the case of even-indexed chunks (1-indexed).            | [[['a', 'b', 'c', '1', '2', 'D', '5']], [['a', 'b', 'c', '1', '2', 'D', '5'], ['A', 'B', 'C', '1', '2', 'd', '5'], ['a', 'b', 'c', '1']], [['a', 'b', 'C', '3', '4', 'd', '3'], ['A', 'B', 'c', '3', '4', 'D', '3'], ['a', 'b', 'C', '3']]]
               F        Flatten.                                                     | [['a', 'b', 'c', '1', '2', 'D', '5'], ['a', 'b', 'c', '1', '2', 'D', '5', 'A', 'B', 'C', '1', '2', 'd', '5', 'a', 'b', 'c', '1'], ['a', 'b', 'C', '3', '4', 'd', '3', 'A', 'B', 'c', '3', '4', 'D', '3', 'a', 'b', 'C', '3']]
                n       Vectorized inequality with y.                                | [[[0, 0, 1, 1, 1, 1, 1]], [[1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], [[1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1]]]
                  §     After ending the map, sum each bool (0 or 1) array.          | [[5], [17], [14]]
                   Ṁ    Maximum.                                                     | 17