The transcript may have been cropped, but from what little is presented Stobart are cautioned about the BA pushing back. The first the BA appear to know is being stopped by the ground crew. Where was ATC trying to call Speedbird?
Yes, the Speedbird crew appear irked by the situation, rightly or wrongly; but I wouldn't say they're unprofessional about raising their concern. From another viewpoint, they also give the controller advance notification that they consider safety was eroded and the ATC has an opportunity to recall as much of her perception of the situation as possible, rather than finding out several weeks later and not have a complete picture of events.
The ignorant rubbish from other crews is indicative of poor discipline that's invading the modern cockpit. It's a poor reflection on the others, not the ATC or Speedbird. Tall poppy syndrome.