BUG: Fix mixed datetime dtype inference

Author: dsaxton

doc/source/whatsnew/v1.1.0.rst

@@ -461,6 +461,7 @@ Datetimelike
 - Bug in :meth:`DatetimeIndex.to_period` not infering the frequency when called with no arguments (:issue:`33358`)
 - Bug in :meth:`DatetimeIndex.tz_localize` incorrectly retaining ``freq`` in some cases where the original freq is no longer valid (:issue:`30511`)
 - Bug in :meth:`DatetimeIndex.intersection` losing ``freq`` and timezone in some cases (:issue:`33604`)
+- Bug in :meth:`Index.get_indexer` where incorrect output would be returned for mixed datetime-like targets (:issues:`33741`)
 
 Timedelta
 ^^^^^^^^^

pandas/_libs/lib.pyx

@@ -1373,6 +1373,8 @@ def infer_dtype(value: object, skipna: bool = True) -> str:
     elif PyDateTime_Check(val):
         if is_datetime_array(values):
             return "datetime"
+        if is_date_array(values):
+            return "date"
 
     elif PyDate_Check(val):
         if is_date_array(values, skipna=skipna):

pandas/tests/dtypes/test_inference.py

@@ -1097,6 +1097,18 @@ def test_date(self):
         result = lib.infer_dtype(dates, skipna=True)
         assert result == "date"
 
+    @pytest.mark.parametrize(
+        "values",
+        [
+            [date(2020, 1, 1), pd.Timestamp("2020-01-01")],
+            [pd.Timestamp("2020-01-01"), date(2020, 1, 1)],
+        ],
+    )
+    def test_infer_dtype_date_order_invariant(self, values):
+        # https://github.com/pandas-dev/pandas/issues/33741
+        result = lib.infer_dtype(values, skipna=True)
+        assert result == "date"
+
     def test_is_numeric_array(self):
 
         assert lib.is_float_array(np.array([1, 2.0]))

pandas/tests/indexes/datetimes/test_indexing.py

@@ -1,4 +1,4 @@
-from datetime import datetime, time, timedelta
+from datetime import datetime, date, time, timedelta
 
 import numpy as np
 import pytest
@@ -547,6 +547,22 @@ def test_get_indexer(self):
         with pytest.raises(ValueError, match="abbreviation w/o a number"):
             idx.get_indexer(idx[[0]], method="nearest", tolerance="foo")
 
+    @pytest.mark.parametrize(
+        "target",
+        [
+            [date(2020, 1, 1), pd.Timestamp("2020-01-02")],
+            [pd.Timestamp("2020-01-01"), date(2020, 1, 2)],
+        ],
+    )
+    def test_get_indexer_mixed_dtypes(self, target):
+        # https://github.com/pandas-dev/pandas/issues/33741
+        values = pd.DatetimeIndex(
+            [pd.Timestamp("2020-01-01"), pd.Timestamp("2020-01-02")]
+        )
+        result = values.get_indexer(target)
+        expected = np.array([0, 1])
+        tm.assert_numpy_array_equal(result, expected)
+
 
 class TestMaybeCastSliceBound:
     def test_maybe_cast_slice_bounds_empty(self):