Backport PR #48987 on branch 1.5.x (REG: Fix regression in assert_frame_equal for categorical and check_like) (#48997)

Backport PR #48987: REG: Fix regression in assert_frame_equal for categorical and check_like

Co-authored-by: Patrick Hoefler <61934744+phofl@users.noreply.github.com>

Author: meeseeksmachine

doc/source/whatsnew/v1.5.1.rst

@@ -79,6 +79,7 @@ Fixed regressions
 - Fixed performance regression in :func:`factorize` when ``na_sentinel`` is not ``None`` and ``sort=False`` (:issue:`48620`)
 - Fixed regression causing an ``AttributeError`` during warning emitted if the provided table name in :meth:`DataFrame.to_sql` and the table name actually used in the database do not match (:issue:`48733`)
 - Fixed regression in :func:`to_datetime` when ``arg`` was a date string with nanosecond and ``format`` contained ``%f`` would raise a ``ValueError`` (:issue:`48767`)
+- Fixed regression in :func:`assert_frame_equal` raising for :class:`MultiIndex` with :class:`Categorical` and ``check_like=True`` (:issue:`48975`)
 - Fixed regression in :meth:`DataFrame.fillna` replacing wrong values for ``datetime64[ns]`` dtype and ``inplace=True`` (:issue:`48863`)
 - Fixed :meth:`.DataFrameGroupBy.size` not returning a Series when ``axis=1`` (:issue:`48738`)
 - Fixed Regression in :meth:`DataFrameGroupBy.apply` when user defined function is called on an empty dataframe (:issue:`47985`)

pandas/core/indexes/api.py

@@ -189,6 +189,9 @@ def safe_sort_index(index: Index) -> Index:
     except TypeError:
         pass
     else:
+        if isinstance(array_sorted, MultiIndex):
+            return array_sorted
+
         array_sorted = cast(np.ndarray, array_sorted)
         if isinstance(index, MultiIndex):
             index = MultiIndex.from_tuples(array_sorted, names=index.names)

pandas/tests/util/test_assert_frame_equal.py

@@ -342,3 +342,26 @@ def test_assert_frame_equal_checking_allow_dups_flag():
 
     with pytest.raises(AssertionError, match="allows_duplicate_labels"):
         tm.assert_frame_equal(left, right, check_flags=True)
+
+
+def test_assert_frame_equal_check_like_categorical_midx():
+    # GH#48975
+    left = DataFrame(
+        [[1], [2], [3]],
+        index=pd.MultiIndex.from_arrays(
+            [
+                pd.Categorical(["a", "b", "c"]),
+                pd.Categorical(["a", "b", "c"]),
+            ]
+        ),
+    )
+    right = DataFrame(
+        [[3], [2], [1]],
+        index=pd.MultiIndex.from_arrays(
+            [
+                pd.Categorical(["c", "b", "a"]),
+                pd.Categorical(["c", "b", "a"]),
+            ]
+        ),
+    )
+    tm.assert_frame_equal(left, right, check_like=True)