diff --git a/pandas/core/arrays/categorical.py b/pandas/core/arrays/categorical.py
index 40a169d03f39c..71a3ccfb64024 100644
--- a/pandas/core/arrays/categorical.py
+++ b/pandas/core/arrays/categorical.py
@@ -1494,7 +1494,7 @@ def check_for_ordered(self, op):
             )
 
     def _values_for_argsort(self):
-        return self._codes.copy()
+        return self._codes
 
     def argsort(self, ascending=True, kind="quicksort", **kwargs):
         """
diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 6f44b5abf5b04..1cd772a72058d 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -3385,6 +3385,7 @@ def join(self, other, how="left", level=None, return_indexers=False, sort=False)
         -------
         join_index, (left_indexer, right_indexer)
         """
+        other = ensure_index(other)
         self_is_mi = isinstance(self, ABCMultiIndex)
         other_is_mi = isinstance(other, ABCMultiIndex)
 
@@ -3404,8 +3405,6 @@ def join(self, other, how="left", level=None, return_indexers=False, sort=False)
                 other, level, how=how, return_indexers=return_indexers
             )
 
-        other = ensure_index(other)
-
         if len(other) == 0 and how in ("left", "outer"):
             join_index = self._shallow_copy()
             if return_indexers:
@@ -3567,16 +3566,26 @@ def _join_multi(self, other, how, return_indexers=True):
     def _join_non_unique(self, other, how="left", return_indexers=False):
         from pandas.core.reshape.merge import _get_join_indexers
 
+        # We only get here if dtypes match
+        assert self.dtype == other.dtype
+
+        if is_extension_array_dtype(self.dtype):
+            lvalues = self._data._values_for_argsort()
+            rvalues = other._data._values_for_argsort()
+        else:
+            lvalues = self._values
+            rvalues = other._values
+
         left_idx, right_idx = _get_join_indexers(
-            [self._ndarray_values], [other._ndarray_values], how=how, sort=True
+            [lvalues], [rvalues], how=how, sort=True
         )
 
         left_idx = ensure_platform_int(left_idx)
         right_idx = ensure_platform_int(right_idx)
 
-        join_index = np.asarray(self._ndarray_values.take(left_idx))
+        join_index = np.asarray(lvalues.take(left_idx))
         mask = left_idx == -1
-        np.putmask(join_index, mask, other._ndarray_values.take(right_idx))
+        np.putmask(join_index, mask, rvalues.take(right_idx))
 
         join_index = self._wrap_joined_index(join_index, other)
 
@@ -3727,6 +3736,9 @@ def _get_leaf_sorter(labels):
             return join_index
 
     def _join_monotonic(self, other, how="left", return_indexers=False):
+        # We only get here with matching dtypes
+        assert other.dtype == self.dtype
+
         if self.equals(other):
             ret_index = other if how == "right" else self
             if return_indexers:
@@ -3734,8 +3746,12 @@ def _join_monotonic(self, other, how="left", return_indexers=False):
             else:
                 return ret_index
 
-        sv = self._ndarray_values
-        ov = other._ndarray_values
+        if is_extension_array_dtype(self.dtype):
+            sv = self._data._values_for_argsort()
+            ov = other._data._values_for_argsort()
+        else:
+            sv = self._values
+            ov = other._values
 
         if self.is_unique and other.is_unique:
             # We can perform much better than the general case