Backport PR #53102 on branch 2.0.x (REGR: MultiIndex.join not resorti…

…ng levels of new index) (#53113)

Backport PR #53102: REGR: MultiIndex.join not resorting levels of new index

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

doc/source/whatsnew/v2.0.2.rst

@@ -15,6 +15,8 @@ Fixed regressions
 ~~~~~~~~~~~~~~~~~
 - Fixed regression in :meth:`DataFrame.loc` losing :class:`MultiIndex` name when enlarging object (:issue:`53053`)
 - Fixed regression in :meth:`DataFrame.to_string` printing a backslash at the end of the first row of data, instead of headers, when the DataFrame doesn't fit the line width (:issue:`53054`)
+- Fixed regression in :meth:`MultiIndex.join` returning levels in wrong order (:issue:`53093`)
+-
 
 .. ---------------------------------------------------------------------------
 .. _whatsnew_202.bug_fixes:

pandas/core/indexes/base.py

@@ -4877,7 +4877,7 @@ def _wrap_joined_index(
             mask = lidx == -1
             join_idx = self.take(lidx)
             right = other.take(ridx)
-            join_index = join_idx.putmask(mask, right)
+            join_index = join_idx.putmask(mask, right)._sort_levels_monotonic()
             return join_index.set_names(name)  # type: ignore[return-value]
         else:
             name = get_op_result_name(self, other)

pandas/tests/indexes/multi/test_join.py

@@ -257,3 +257,15 @@ def test_join_dtypes_all_nan(any_numeric_ea_dtype):
         ]
     )
     tm.assert_index_equal(result, expected)
+
+
+def test_join_index_levels():
+    # GH#53093
+    midx = midx = MultiIndex.from_tuples([("a", "2019-02-01"), ("a", "2019-02-01")])
+    midx2 = MultiIndex.from_tuples([("a", "2019-01-31")])
+    result = midx.join(midx2, how="outer")
+    expected = MultiIndex.from_tuples(
+        [("a", "2019-01-31"), ("a", "2019-02-01"), ("a", "2019-02-01")]
+    )
+    tm.assert_index_equal(result.levels[1], expected.levels[1])
+    tm.assert_index_equal(result, expected)