One of the things Karl Friday is saying (paraphrasing slightly) is that if you mix some bits of Aikido into Kashima Shinryu the result is no longer Kashima Shinryu. Do you have a criteria for the opposite, i.e: "if you mix some bits of Kashima Shinryu into Aikido, it is no longer Aikido" ?
I think the point is more that it is impossible to "mix some bits of Aikido into Kashima Shinryu." Kashima Shinryu is exactly one thing: a transmission of principals using a very specific structure and progression of training methodology, from the founder through licensed instructors to the students they choose to take on and teach.
It isn't that "mixing bits" of Aikido somehow spoils the "brew." it is that there is simply no part of Kashima Shinryu training where a student goes "what if I move like this instead of what I am supposed to do in the kata?" That's just not part of the program. And it would be pointless, because you would be trying to bypass learning something you are supposed to be learning. You are off the kata such that you are not priming yourself to understand a gokui. My take on it, anyway.
The reverse would be fine in most styles of Aikido training IMO. I'm not sure whether to characterize Iwama and Yoshinkan training methods as kata- and gokui-based in a similar way to koryu. If training involves doing certain things as a means to elicit a certain quality of movement or sensitivity in the practitioner, as opposed to obtaining a certain result, I wouldn't mess with it.