diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 802fd0feedb48..1c6b8f71e2a22 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -3246,33 +3246,13 @@ def symmetric_difference(self, other, result_name=None, sort=None):
         if result_name is None:
             result_name = result_name_update
 
-        if not self._should_compare(other):
-            return self.union(other, sort=sort).rename(result_name)
-        elif not is_dtype_equal(self.dtype, other.dtype):
-            dtype = find_common_type([self.dtype, other.dtype])
-            this = self.astype(dtype, copy=False)
-            that = other.astype(dtype, copy=False)
-            return this.symmetric_difference(that, sort=sort).rename(result_name)
-
-        this = self._get_unique_index()
-        other = other._get_unique_index()
-        indexer = this.get_indexer_for(other)
+        left = self.difference(other, sort=False)
+        right = other.difference(self, sort=False)
+        result = left.union(right, sort=sort)
 
-        # {this} minus {other}
-        common_indexer = indexer.take((indexer != -1).nonzero()[0])
-        left_indexer = np.setdiff1d(
-            np.arange(this.size), common_indexer, assume_unique=True
-        )
-        left_diff = this._values.take(left_indexer)
-
-        # {other} minus {this}
-        right_indexer = (indexer == -1).nonzero()[0]
-        right_diff = other._values.take(right_indexer)
-
-        the_diff = concat_compat([left_diff, right_diff])
-        the_diff = _maybe_try_sort(the_diff, sort)
-
-        return Index(the_diff, name=result_name)
+        if result_name is not None:
+            result = result.rename(result_name)
+        return result
 
     @final
     def _assert_can_do_setop(self, other) -> bool:
diff --git a/pandas/core/indexes/category.py b/pandas/core/indexes/category.py
index 554cf33e22555..ab44ae832c791 100644
--- a/pandas/core/indexes/category.py
+++ b/pandas/core/indexes/category.py
@@ -269,6 +269,10 @@ def _is_dtype_compat(self, other) -> Categorical:
                 raise TypeError(
                     "categories must match existing categories when appending"
                 )
+
+        elif other._is_multi:
+            # preempt raising NotImplementedError in isna call
+            raise TypeError("MultiIndex is not dtype-compatible with CategoricalIndex")
         else:
             values = other
 
diff --git a/pandas/core/indexes/datetimelike.py b/pandas/core/indexes/datetimelike.py
index 6c8c175b51ecf..df7fae0763c42 100644
--- a/pandas/core/indexes/datetimelike.py
+++ b/pandas/core/indexes/datetimelike.py
@@ -60,7 +60,6 @@
     inherit_names,
     make_wrapped_arith_op,
 )
-from pandas.core.indexes.numeric import Int64Index
 from pandas.core.tools.timedeltas import to_timedelta
 
 if TYPE_CHECKING:
@@ -779,11 +778,7 @@ def _union(self, other, sort):
             #  that result.freq == self.freq
             return result
         else:
-            i8self = Int64Index._simple_new(self.asi8)
-            i8other = Int64Index._simple_new(other.asi8)
-            i8result = i8self._union(i8other, sort=sort)
-            result = type(self)(i8result, dtype=self.dtype, freq="infer")
-            return result
+            return super()._union(other, sort=sort)._with_freq("infer")
 
     # --------------------------------------------------------------------
     # Join Methods
diff --git a/pandas/core/indexes/multi.py b/pandas/core/indexes/multi.py
index 07795a9f09c2a..8956f822260f3 100644
--- a/pandas/core/indexes/multi.py
+++ b/pandas/core/indexes/multi.py
@@ -3680,9 +3680,9 @@ def symmetric_difference(self, other, result_name=None, sort=None):
             return type(self)(
                 levels=[[] for _ in range(self.nlevels)],
                 codes=[[] for _ in range(self.nlevels)],
-                names=tups.name,
+                names=tups.names,
             )
-        return type(self).from_tuples(tups, names=tups.name)
+        return tups
 
     # --------------------------------------------------------------------
 
diff --git a/pandas/core/indexes/range.py b/pandas/core/indexes/range.py
index ead1a2a4a544b..da6c061040282 100644
--- a/pandas/core/indexes/range.py
+++ b/pandas/core/indexes/range.py
@@ -730,18 +730,6 @@ def _difference(self, other, sort=None):
             new_index = new_index[::-1]
         return new_index
 
-    def symmetric_difference(self, other, result_name: Hashable = None, sort=None):
-        if not isinstance(other, RangeIndex) or sort is not None:
-            return super().symmetric_difference(other, result_name, sort)
-
-        left = self.difference(other)
-        right = other.difference(self)
-        result = left.union(right)
-
-        if result_name is not None:
-            result = result.rename(result_name)
-        return result
-
     # --------------------------------------------------------------------
 
     def _concat(self, indexes: list[Index], name: Hashable) -> Index:
diff --git a/pandas/tests/indexes/categorical/test_equals.py b/pandas/tests/indexes/categorical/test_equals.py
index 2648155c938b0..1ed8f3a903439 100644
--- a/pandas/tests/indexes/categorical/test_equals.py
+++ b/pandas/tests/indexes/categorical/test_equals.py
@@ -5,6 +5,7 @@
     Categorical,
     CategoricalIndex,
     Index,
+    MultiIndex,
 )
 
 
@@ -79,3 +80,11 @@ def test_equals_non_category(self):
         other = Index(["A", "B", "D", np.nan])
 
         assert not ci.equals(other)
+
+    def test_equals_multiindex(self):
+        # dont raise NotImplementedError when calling is_dtype_compat
+
+        mi = MultiIndex.from_arrays([["A", "B", "C", "D"], range(4)])
+        ci = mi.to_flat_index().astype("category")
+
+        assert not ci.equals(mi)