BUG: join not working correctly with MultiIndex and one dimension categorical

doc/source/whatsnew/v1.3.0.rst

@@ -266,7 +266,7 @@ Groupby/resample/rolling
 Reshaping
 ^^^^^^^^^
 
--
+- Bug in :meth:`DataFrame.join` not assigning values correctly when having :class:`MultiIndex` where at least one dimension is from dtype ``Categorical`` with non-alphabetically sorted categories (:issue:`38502`)
 -
 
 Sparse

pandas/core/indexes/base.py

@@ -3683,7 +3683,16 @@ def join(self, other, how="left", level=None, return_indexers=False, sort=False)
                 return self._join_non_unique(
                     other, how=how, return_indexers=return_indexers
                 )
-        elif self.is_monotonic and other.is_monotonic:
+        elif (
+            self.is_monotonic
+            and other.is_monotonic
+            and (
+                not isinstance(self, ABCMultiIndex)
+                or not any(is_categorical_dtype(dtype) for dtype in self.dtypes)
+            )
+        ):
+            # Categorical is monotonic if data are ordered as categories, but join can
+            #  not handle this in case of not alphabetically monotonic GH#38502
             try:
                 return self._join_monotonic(
                     other, how=how, return_indexers=return_indexers

pandas/tests/reshape/merge/test_join.py

@@ -2,7 +2,7 @@
 import pytest
 
 import pandas as pd
-from pandas import DataFrame, Index, MultiIndex, Series, concat, merge
+from pandas import Categorical, DataFrame, Index, MultiIndex, Series, concat, merge
 import pandas._testing as tm
 from pandas.tests.reshape.merge.test_merge import NGROUPS, N, get_test_data
 
@@ -815,3 +815,32 @@ def test_join_cross(input_col, output_cols):
     result = left.join(right, how="cross", lsuffix="_x", rsuffix="_y")
     expected = DataFrame({output_cols[0]: [1, 1, 3, 3], output_cols[1]: [3, 4, 3, 4]})
     tm.assert_frame_equal(result, expected)
+
+
+def test_join_multiindex_not_alphabetical_categorical():
+    # GH#38502
+    left = DataFrame(
+        {
+            "first": ["A", "A"],
+            "second": Categorical(["Y", "X"], categories=["Y", "X"]),
+            "value": [1, 2],
+        }
+    ).set_index(["first", "second"])
+    right = DataFrame(
+        {
+            "first": ["A", "A", "B"],
+            "second": Categorical(["Y", "X", "X"], categories=["Y", "X"]),
+            "value": [3, 4, 5],
+        }
+    ).set_index(["first", "second"])
+    result = left.join(right, lsuffix="_left", rsuffix="_right")
+
+    expected = DataFrame(
+        {
+            "first": ["A", "A"],
+            "second": Categorical(["Y", "X"], categories=["Y", "X"]),
+            "value_left": [1, 2],
+            "value_right": [3, 4],
+        }
+    ).set_index(["first", "second"])
+    tm.assert_frame_equal(result, expected)