diff --git a/pandas/core/indexes/datetimelike.py b/pandas/core/indexes/datetimelike.py
index 894e1d95a17bc..7889829516f7f 100644
--- a/pandas/core/indexes/datetimelike.py
+++ b/pandas/core/indexes/datetimelike.py
@@ -22,7 +22,6 @@
     is_list_like,
     is_period_dtype,
     is_scalar,
-    needs_i8_conversion,
 )
 from pandas.core.dtypes.concat import concat_compat
 from pandas.core.dtypes.generic import ABCIndex, ABCIndexClass, ABCSeries
@@ -484,7 +483,7 @@ def where(self, cond, other=None):
 
             if is_categorical_dtype(other):
                 # e.g. we have a Categorical holding self.dtype
-                if needs_i8_conversion(other.categories):
+                if is_dtype_equal(other.categories.dtype, self.dtype):
                     other = other._internal_get_values()
 
             if not is_dtype_equal(self.dtype, other.dtype):
diff --git a/pandas/core/internals/blocks.py b/pandas/core/internals/blocks.py
index 024d3b205df77..87892a804dac3 100644
--- a/pandas/core/internals/blocks.py
+++ b/pandas/core/internals/blocks.py
@@ -2284,11 +2284,7 @@ def to_native_types(
         return np.atleast_2d(result)
 
     def should_store(self, value) -> bool:
-        return (
-            issubclass(value.dtype.type, np.datetime64)
-            and not is_datetime64tz_dtype(value)
-            and not is_extension_array_dtype(value)
-        )
+        return is_datetime64_dtype(value.dtype)
 
     def set(self, locs, values):
         """
@@ -2536,9 +2532,7 @@ def fillna(self, value, **kwargs):
         return super().fillna(value, **kwargs)
 
     def should_store(self, value) -> bool:
-        return issubclass(
-            value.dtype.type, np.timedelta64
-        ) and not is_extension_array_dtype(value)
+        return is_timedelta64_dtype(value.dtype)
 
     def to_native_types(self, slicer=None, na_rep=None, quoting=None, **kwargs):
         """ convert to our native types format, slicing if desired """