// I wonder how different the response on AB would have been had the same insults been made towards the previous President? //
Very possibly they were, but the point is that they remained private. What's inappropriate about Trump's tweets is how public they are. Up until what our ambassador said was leaked then we never knew, and probably wouldn't even have cared. What he thought about the US President was secret, confidential, and only a small part of the picture used to shape our relationship with the US. What Trump tweets is public, and since he isn't a minor diplomatic official but the actual President, then what he says is bound to carry a great deal more weight in shaping US/UK relations.