diff --git a/jax/_src/custom_derivatives.py b/jax/_src/custom_derivatives.py
index 522a3b779bb3..9c112970aea7 100644
--- a/jax/_src/custom_derivatives.py
+++ b/jax/_src/custom_derivatives.py
@@ -772,8 +772,7 @@ def append(x, d):
       results.append(Zero(ct.aval))
     else:
       if (not core.typecompat(a.at_least_vspace(), a_ := core.get_aval(ct))
-          # TODO(mattjj): don't skip check with extended dtype tangent types
-          and not dtypes.issubdtype(a_.dtype, dtypes.extended)):
+          and not _temporary_dtype_exception(a, a_)):
         msg = ("Custom VJP bwd rule must produce an output with the same "
                "shape/dtypes as the args tuple of the primal function, but at "
                f"output{keystr(kp)} the bwd rule produced an output of "
@@ -783,6 +782,14 @@ def append(x, d):
       results.append(ct)
   yield results
 
+# TODO(mattjj): remove both these exceptions to cotangent compatibility check
+def _temporary_dtype_exception(a, a_) -> bool:
+  if isinstance(a, core.ShapedArray) and isinstance(a_, core.ShapedArray):
+    return (a.shape == a_.shape and
+            (dtypes.issubdtype(a_.dtype, dtypes.extended) or
+             dtypes.issubdtype(a.dtype, dtypes.np.inexact)))
+  return False
+
 
 class CustomVJPCallPrimitive(core.CallPrimitive):
   initial_style: core.Primitive