BUG: fix union_indexes not supporting sort=False for Index subclasses

doc/source/whatsnew/v1.1.0.rst

@@ -974,6 +974,7 @@ Indexing
 - Bug in :meth:`DataFrame.loc` with dictionary of values changes columns with dtype of ``int`` to ``float`` (:issue:`34573`)
 - Bug in :meth:`Series.loc` when used with a :class:`MultiIndex` would raise an IndexingError when accessing a None value (:issue:`34318`)
 - Bug in :meth:`DataFrame.reset_index` and :meth:`Series.reset_index` would not preserve data types on an empty :class:`DataFrame` or :class:`Series` with a :class:`MultiIndex` (:issue:`19602`)
+- Bug in :func:`pandas.core.indexes.api.union_indexes` would lead to :meth:`DataFrame.append` sorting columns even when ``sort=False`` is specified (:issue:`35092`)
 
 Missing
 ^^^^^^^

pandas/core/indexes/api.py

@@ -206,6 +206,17 @@ def conv(i):
 
         return Index(lib.fast_unique_multiple_list([conv(i) for i in inds], sort=sort))
 
+    # GH 35092. Detect if we have an Index type, for which the sort
+    # setting doesn't make sense
+    ind_types = list({type(index) for index in indexes})
+    if any(
+        ind_type in [MultiIndex, RangeIndex, DatetimeIndex, CategoricalIndex]
+        for ind_type in ind_types
+    ):
+        ignore_sort = True
+    else:
+        ignore_sort = False
+
     if kind == "special":
         result = indexes[0]
 
@@ -214,7 +225,11 @@ def conv(i):
             return result.union_many(indexes[1:])
         else:
             for other in indexes[1:]:
-                result = result.union(other)
+                # GH 35092. Pass sort to Index.union
+                # Index.union expects sort=None instead of sort=True
+                if sort:
+                    sort = None
+                result = result.union(other, sort=sort)
             return result
     elif kind == "array":
         index = indexes[0]

pandas/tests/indexes/test_common.py

@@ -13,8 +13,9 @@
 from pandas.core.dtypes.common import is_period_dtype, needs_i8_conversion
 
 import pandas as pd
-from pandas import CategoricalIndex, MultiIndex, RangeIndex
+from pandas import CategoricalIndex, Index, MultiIndex, RangeIndex
 import pandas._testing as tm
+from pandas.core.indexes.api import union_indexes
 
 
 class TestCommon:
@@ -395,3 +396,15 @@ def test_astype_preserves_name(self, index, dtype, copy):
             assert result.names == index.names
         else:
             assert result.name == index.name
+
+
+@pytest.mark.parametrize("exp_arr, sort", [([0, 1, 4, 3], False), ([0, 1, 3, 4], True)])
+@pytest.mark.parametrize("dtype", ["int8", "int16", "int32", "int64"])
+def test_union_index_no_sort(exp_arr, sort, dtype):
+    # GH 35092. Check that we don't sort with sort=False
+    ind1 = Index([0, 1], dtype=dtype)
+    ind2 = Index([4, 3], dtype=dtype)
+
+    expected = Index(exp_arr, dtype=dtype)
+    result = union_indexes([ind1, ind2], sort=sort)
+    tm.assert_index_equal(result, expected)