Is this skew symmetry?
APL (Dyalog Unicode), 44 34 bytesSBCS

crossed out 44 is still regular 44 ;(

Hats off to @Bubbler, @ngn and @TesselatingHeckler as they managed to shave some bytes off of my solution, more or less independently but coming up with the same simplifications.



{1∊(l↓⍵)⍷⍨a/⍨∨⌿' '≠a←⊖⍵↑⍨l←2÷⍨≢⍵}⍉


Try it online!

Now I'll explain how it works:

{                                   }⍉  ⍝ We define a monadic function that we apply right after transposing (⍉) the input [this means we will be operating on columns instead of rows]
                              2÷⍨≢⍵    ⍝ Start by finding how many  columns the input has (≢),split that in half (2÷⍨)
                            l←          ⍝   and assign that to l (l←) ...
                        ⍵↑⍨            ⍝ Using it right away to take (↑⍨) l columns from the original input ⍵
                       ⊖               ⍝   which we then reverse (⊖) [effectively flipping the columns upside down]
                     a←                 ⍝   and assign to a (a←)
                 ' '≠                   ⍝ We then compare each character in a to ' '
               ∨⌿                       ⍝   and we "interleave" the logical OR (∨) over the columns (⌿) [to find columns where at least one character is different from ' ']
           a/⍨                          ⍝   finally selecting those columns from a (a/⍨)
         ⍷⍨                             ⍝ Now we superimpose that piece of the original character matrix over all possible locations
   (l↓⍵)                               ⍝   of the columns of ⍵ that remain after we drop (↓) the first l columns [i.e. we take the second half of the columns]
 1∊                                    ⍝   and we look for matches by checking if there is a 1 (Truthy) in any position (∊)