COMPAT: work around deprecation warning on non-equal dtype comparisons

closes pandas-dev#20011

Author: jreback

pandas/core/indexes/base.py

@@ -95,13 +95,19 @@ def cmp_method(self, other):
         if needs_i8_conversion(self) and needs_i8_conversion(other):
             return self._evaluate_compare(other, op)
 
+        other = np.asarray(other)
         if is_object_dtype(self) and self.nlevels == 1:
             # don't pass MultiIndex
             with np.errstate(all='ignore'):
                 result = ops._comp_method_OBJECT_ARRAY(op, self.values, other)
+
+        elif self.values.dtype.type != other.dtype.type:
+            # short-circuit on dtype inequity
+            result = op is not operator.eq
+
         else:
             with np.errstate(all='ignore'):
-                result = op(self.values, np.asarray(other))
+                result = op(self.values, other)
 
         # technically we could support bool dtyped Index
         # for now just return the indexing array directly