BUG: get_indexer rountripping through string dtype

Author: phofl

doc/source/whatsnew/v2.1.4.rst

@@ -22,6 +22,7 @@ Fixed regressions
 Bug fixes
 ~~~~~~~~~
 - Bug in :class:`Series` constructor raising DeprecationWarning when ``index`` is a list of :class:`Series` (:issue:`55228`)
+- Fixed bug in :meth:`Index.get_indexer` round-tripping through string dtype when ``infer_string`` is enabled (:issue:`55834`)
 -
 
 .. ---------------------------------------------------------------------------

pandas/core/indexes/base.py

@@ -6580,6 +6580,9 @@ def _maybe_cast_listlike_indexer(self, target) -> Index:
         """
         Analogue to maybe_cast_indexer for get_indexer instead of get_loc.
         """
+        if not hasattr(target, "dtype") and self.dtype == object:
+            # Avoid inference for object since we are casting back later anyway
+            return Index(target, dtype=self.dtype)
         return ensure_index(target)
 
     @final

pandas/tests/indexes/object/test_indexing.py

@@ -4,6 +4,7 @@
 import pytest
 
 from pandas._libs.missing import is_matching_na
+import pandas.util._test_decorators as td
 
 import pandas as pd
 from pandas import Index
@@ -55,6 +56,14 @@ def test_get_indexer_with_NA_values(
         expected = np.array([0, 1, -1], dtype=np.intp)
         tm.assert_numpy_array_equal(result, expected)
 
+    @td.skip_if_no("pyarrow")
+    def test_get_indexer_infer_string_missing_values(self):
+        # GH#55834
+        idx = Index(["a", "b", None], dtype="object")
+        result = idx.get_indexer([None, "x"])
+        expected = np.array([2, -1])
+        tm.assert_numpy_array_equal(result, expected)
+
 
 class TestGetIndexerNonUnique:
     def test_get_indexer_non_unique_nas(self, nulls_fixture):