Just like tabs vs spaces animosity has largely been ended through the use of auto formatters, I think there is a technological solution as well for this.
Create an auto responder for “Hi” and “Hello” that will just echo it back and not cause a notification.
So it becomes:
Other person: Hi
Auto responder: Hi
(No chat notification)
Other person: <Asks question>
(You get chat notifications, if enabled)
You: Answer question
This seems to solve most of the issues, and should be rather simple to implement.