Backport PR #47325 on branch 1.4.x (REGR: Avoid regression warning with ea dtype and assert_index_equal order False)

doc/source/whatsnew/v1.4.3.rst

@@ -24,6 +24,7 @@ Fixed regressions
 - Fixed regression in :func:`read_csv` with ``index_col=False`` identifying first row as index names when ``header=None`` (:issue:`46955`)
 - Fixed regression in :meth:`.DataFrameGroupBy.agg` when used with list-likes or dict-likes and ``axis=1`` that would give incorrect results; now raises ``NotImplementedError`` (:issue:`46995`)
 - Fixed regression in :meth:`DataFrame.resample` and :meth:`DataFrame.rolling` when used with list-likes or dict-likes and ``axis=1`` that would raise an unintuitive error message; now raises ``NotImplementedError`` (:issue:`46904`)
+- Fixed regression in :func:`assert_index_equal` when ``check_order=False`` and :class:`Index` has extension or object dtype (:issue:`47207`)
 - Fixed regression in :func:`read_excel` returning ints as floats on certain input sheets (:issue:`46988`)
 - Fixed regression in :meth:`DataFrame.shift` when ``axis`` is ``columns`` and ``fill_value`` is absent, ``freq`` is ignored (:issue:`47039`)
 

pandas/_testing/asserters.py

@@ -374,8 +374,8 @@ def _get_ilevel_values(index, level):
 
     # If order doesn't matter then sort the index entries
     if not check_order:
-        left = Index(safe_sort(left))
-        right = Index(safe_sort(right))
+        left = Index(safe_sort(left), dtype=left.dtype)
+        right = Index(safe_sort(right), dtype=right.dtype)
 
     # MultiIndex special comparison for little-friendly error messages
     if left.nlevels > 1:

pandas/tests/util/test_assert_index_equal.py

@@ -242,3 +242,17 @@ def test_assert_index_equal_mixed_dtype():
     # GH#39168
     idx = Index(["foo", "bar", 42])
     tm.assert_index_equal(idx, idx, check_order=False)
+
+
+def test_assert_index_equal_ea_dtype_order_false(any_numeric_ea_dtype):
+    # GH#47207
+    idx1 = Index([1, 3], dtype=any_numeric_ea_dtype)
+    idx2 = Index([3, 1], dtype=any_numeric_ea_dtype)
+    tm.assert_index_equal(idx1, idx2, check_order=False)
+
+
+def test_assert_index_equal_object_ints_order_false():
+    # GH#47207
+    idx1 = Index([1, 3], dtype="object")
+    idx2 = Index([3, 1], dtype="object")
+    tm.assert_index_equal(idx1, idx2, check_order=False)