BUG: join not working correctly with MultiIndex and one dimension categorical (pandas-dev#38621)

Author: phofl

doc/source/whatsnew/v1.3.0.rst

@@ -319,6 +319,7 @@ Reshaping
 - Bug in :meth:`DataFrame.unstack` with missing levels led to incorrect index names (:issue:`37510`)
 - Bug in :func:`join` over :class:`MultiIndex` returned wrong result, when one of both indexes had only one level (:issue:`36909`)
 - :meth:`merge_asof` raises ``ValueError`` instead of cryptic ``TypeError`` in case of non-numerical merge columns (:issue:`29130`)
+- 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

@@ -3850,7 +3850,16 @@ 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 lexicographically monotonic GH#38502
             try:
                 return self._join_monotonic(
                     other, how=how, return_indexers=return_indexers

pandas/tests/reshape/merge/test_join.py

@@ -2,7 +2,16 @@
 import pytest
 
 import pandas as pd
-from pandas import DataFrame, Index, MultiIndex, Series, concat, merge
+from pandas import (
+    Categorical,
+    DataFrame,
+    Index,
+    MultiIndex,
+    Series,
+    Timestamp,
+    concat,
+    merge,
+)
 import pandas._testing as tm
 from pandas.tests.reshape.merge.test_merge import NGROUPS, N, get_test_data
 
@@ -693,8 +702,8 @@ def test_join_datetime_string(self):
         result = dfb.join(dfa.set_index(["x", "y"]), on=["x", "y"])
         expected = DataFrame(
             [
-                [pd.Timestamp("2012-08-02 00:00:00"), "J", 1, 15],
-                [pd.Timestamp("2013-04-06 00:00:00"), "L", 2, 20],
+                [Timestamp("2012-08-02 00:00:00"), "J", 1, 15],
+                [Timestamp("2013-04-06 00:00:00"), "L", 2, 20],
             ],
             index=[2, 4],
             columns=["x", "y", "z", "a"],
@@ -831,3 +840,44 @@ def test_join_multiindex_one_level(join_type):
         index=pd.MultiIndex.from_tuples([(2, 1)], names=["b", "a"]),
     )
     tm.assert_frame_equal(result, expected)
+
+
+@pytest.mark.parametrize(
+    "categories, values",
+    [
+        (["Y", "X"], ["Y", "X", "X"]),
+        ([2, 1], [2, 1, 1]),
+        ([2.5, 1.5], [2.5, 1.5, 1.5]),
+        (
+            [Timestamp("2020-12-31"), Timestamp("2019-12-31")],
+            [Timestamp("2020-12-31"), Timestamp("2019-12-31"), Timestamp("2019-12-31")],
+        ),
+    ],
+)
+def test_join_multiindex_not_alphabetical_categorical(categories, values):
+    # GH#38502
+    left = DataFrame(
+        {
+            "first": ["A", "A"],
+            "second": Categorical(categories, categories=categories),
+            "value": [1, 2],
+        }
+    ).set_index(["first", "second"])
+    right = DataFrame(
+        {
+            "first": ["A", "A", "B"],
+            "second": Categorical(values, categories=categories),
+            "value": [3, 4, 5],
+        }
+    ).set_index(["first", "second"])
+    result = left.join(right, lsuffix="_left", rsuffix="_right")
+
+    expected = DataFrame(
+        {
+            "first": ["A", "A"],
+            "second": Categorical(categories, categories=categories),
+            "value_left": [1, 2],
+            "value_right": [3, 4],
+        }
+    ).set_index(["first", "second"])
+    tm.assert_frame_equal(result, expected)