diff --git a/pandas/_testing/__init__.py b/pandas/_testing/__init__.py
index 0be01da1816a2..0a110d69c7a70 100644
--- a/pandas/_testing/__init__.py
+++ b/pandas/_testing/__init__.py
@@ -501,6 +501,8 @@ def shares_memory(left, right) -> bool:
     if isinstance(left, MultiIndex):
         return shares_memory(left._codes, right)
     if isinstance(left, (Index, Series)):
+        if isinstance(right, (Index, Series)):
+            return shares_memory(left._values, right._values)
         return shares_memory(left._values, right)
 
     if isinstance(left, NDArrayBackedExtensionArray):
diff --git a/pandas/conftest.py b/pandas/conftest.py
index 7ad322d050c0f..106518678df6a 100644
--- a/pandas/conftest.py
+++ b/pandas/conftest.py
@@ -600,7 +600,7 @@ def multiindex_year_month_day_dataframe_random_data():
     """
     tdf = DataFrame(
         np.random.default_rng(2).standard_normal((100, 4)),
-        columns=Index(list("ABCD"), dtype=object),
+        columns=Index(list("ABCD")),
         index=date_range("2000-01-01", periods=100, freq="B"),
     )
     ymd = tdf.groupby([lambda x: x.year, lambda x: x.month, lambda x: x.day]).sum()
@@ -787,7 +787,7 @@ def string_series() -> Series:
     """
     return Series(
         np.arange(30, dtype=np.float64) * 1.1,
-        index=Index([f"i_{i}" for i in range(30)], dtype=object),
+        index=Index([f"i_{i}" for i in range(30)]),
         name="series",
     )
 
@@ -798,7 +798,7 @@ def object_series() -> Series:
     Fixture for Series of dtype object with Index of unique strings
     """
     data = [f"foo_{i}" for i in range(30)]
-    index = Index([f"bar_{i}" for i in range(30)], dtype=object)
+    index = Index([f"bar_{i}" for i in range(30)])
     return Series(data, index=index, name="objects", dtype=object)
 
 
@@ -890,8 +890,8 @@ def int_frame() -> DataFrame:
     """
     return DataFrame(
         np.ones((30, 4), dtype=np.int64),
-        index=Index([f"foo_{i}" for i in range(30)], dtype=object),
-        columns=Index(list("ABCD"), dtype=object),
+        index=Index([f"foo_{i}" for i in range(30)]),
+        columns=Index(list("ABCD")),
     )
 
 
diff --git a/pandas/tests/frame/test_reductions.py b/pandas/tests/frame/test_reductions.py
index 05bb603f5c462..30d02f9b5463d 100644
--- a/pandas/tests/frame/test_reductions.py
+++ b/pandas/tests/frame/test_reductions.py
@@ -1047,7 +1047,6 @@ def test_sum_bools(self):
     # ----------------------------------------------------------------------
     # Index of max / min
 
-    @pytest.mark.xfail(using_string_dtype(), reason="TODO(infer_string)")
     @pytest.mark.parametrize("axis", [0, 1])
     def test_idxmin(self, float_frame, int_frame, skipna, axis):
         frame = float_frame
diff --git a/pandas/tests/series/indexing/test_setitem.py b/pandas/tests/series/indexing/test_setitem.py
index 789e3ac752097..d3246f43e991b 100644
--- a/pandas/tests/series/indexing/test_setitem.py
+++ b/pandas/tests/series/indexing/test_setitem.py
@@ -545,7 +545,6 @@ def test_setitem_with_expansion_type_promotion(self):
         expected = Series([Timestamp("2016-01-01"), 3.0, "foo"], index=["a", "b", "c"])
         tm.assert_series_equal(ser, expected)
 
-    @pytest.mark.xfail(using_string_dtype(), reason="TODO(infer_string)")
     def test_setitem_not_contained(self, string_series):
         # set item that's not contained
         ser = string_series.copy()
diff --git a/pandas/tests/series/methods/test_reindex.py b/pandas/tests/series/methods/test_reindex.py
index 068446a5e216b..442d73cadfe47 100644
--- a/pandas/tests/series/methods/test_reindex.py
+++ b/pandas/tests/series/methods/test_reindex.py
@@ -23,7 +23,7 @@
 def test_reindex(datetime_series, string_series):
     identity = string_series.reindex(string_series.index)
 
-    assert np.may_share_memory(string_series.index, identity.index)
+    assert tm.shares_memory(string_series.index, identity.index)
 
     assert identity.index.is_(string_series.index)
     assert identity.index.identical(string_series.index)
diff --git a/pandas/tests/series/methods/test_to_csv.py b/pandas/tests/series/methods/test_to_csv.py
index 6eb7c74d2eca0..3e3eb36112680 100644
--- a/pandas/tests/series/methods/test_to_csv.py
+++ b/pandas/tests/series/methods/test_to_csv.py
@@ -4,8 +4,6 @@
 import numpy as np
 import pytest
 
-from pandas._config import using_string_dtype
-
 import pandas as pd
 from pandas import Series
 import pandas._testing as tm
@@ -26,7 +24,6 @@ def read_csv(self, path, **kwargs):
 
         return out
 
-    @pytest.mark.xfail(using_string_dtype(), reason="TODO(infer_string)")
     def test_from_csv(self, datetime_series, string_series, temp_file):
         # freq doesn't round-trip
         datetime_series.index = datetime_series.index._with_freq(None)