diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index c49f3f9457161..d3abeeebb5195 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -4973,6 +4973,22 @@ def _maybe_promote(self, other: "Index"):
 
         return self, other
 
+    def _get_other_deep(self, other: "Index") -> "Index":
+        dtype = other.dtype
+        if is_categorical_dtype(dtype):
+            # If there is ever a SparseIndex, this could get dispatched
+            #  here too.
+            return dtype.categories
+        return other
+
+    def _should_compare(self, other: "Index") -> bool:
+        """
+        Check if `self == other` can ever have non-False entries.
+        """
+        other = self._get_other_deep(other)
+        dtype = other.dtype
+        return self._is_comparable_dtype(dtype) or is_object_dtype(dtype)
+
     def _is_comparable_dtype(self, dtype: DtypeObj) -> bool:
         """
         Can we compare values of the given dtype to our own?