BUG: Remove special-casing for Python date objects in DatetimeIndex

Author: Aniketsy

pandas/core/indexes/base.py

@@ -6288,6 +6288,10 @@ def _should_compare(self, other: Index) -> bool:
             #  respectively.
             return False
 
+        # GH#62158
+        if self.dtype.kind == "M" and other.inferred_type == "date":
+            return False
+
         dtype = _unpack_nested_dtype(other)
         return (
             self._is_comparable_dtype(dtype)