BUG: fix Dataframe.join with categorical index leads to unexpected reordering (pandas-dev#47881)

* BUG: fix Dataframe.join with categorical index leads to unexpected reordering

* pre-commit issue

Author: xr-chen

doc/source/whatsnew/v1.5.0.rst

@@ -1024,6 +1024,7 @@ Reshaping
 - Bug in :meth:`DataFrame.pivot_table` with ``sort=False`` results in sorted index (:issue:`17041`)
 - Bug in :meth:`concat` when ``axis=1`` and ``sort=False`` where the resulting Index was a :class:`Int64Index` instead of a :class:`RangeIndex` (:issue:`46675`)
 - Bug in :meth:`wide_to_long` raises when ``stubnames`` is missing in columns and ``i`` contains string dtype column (:issue:`46044`)
+- Bug in :meth:`DataFrame.join` with categorical index results in unexpected reordering (:issue:`47812`)
 
 Sparse
 ^^^^^^

pandas/core/indexes/base.py

@@ -4682,6 +4682,7 @@ def join(
                 not isinstance(self, ABCMultiIndex)
                 or not any(is_categorical_dtype(dtype) for dtype in self.dtypes)
             )
+            and not is_categorical_dtype(self.dtype)
         ):
             # Categorical is monotonic if data are ordered as categories, but join can
             #  not handle this in case of not lexicographically monotonic GH#38502

pandas/tests/reshape/merge/test_join.py

@@ -712,6 +712,21 @@ def test_join_datetime_string(self):
         )
         tm.assert_frame_equal(result, expected)
 
+    def test_join_with_categorical_index(self):
+        # GH47812
+        ix = ["a", "b"]
+        id1 = pd.CategoricalIndex(ix, categories=ix)
+        id2 = pd.CategoricalIndex(reversed(ix), categories=reversed(ix))
+
+        df1 = DataFrame({"c1": ix}, index=id1)
+        df2 = DataFrame({"c2": reversed(ix)}, index=id2)
+        result = df1.join(df2)
+        expected = DataFrame(
+            {"c1": ["a", "b"], "c2": ["a", "b"]},
+            index=pd.CategoricalIndex(["a", "b"], categories=["a", "b"]),
+        )
+        tm.assert_frame_equal(result, expected)
+
 
 def _check_join(left, right, result, join_col, how="left", lsuffix="_x", rsuffix="_y"):