I am the same. I will always be plesant to any crew from any other airline. When I flew for the orange lot, we often had positioning crew on domestic flights, I wouldn't let them pay for a thing on my aircraft. It doesn't sound much, but we all do a very similar job, just wearing a different uniform. They were probably at the start or end of a long day, so anything I could do to help out, I would. The same goes for the airline I fly with today.
If there was a rivalry, then I wouldn't talk to half of my family as we all work for different airlines!!!!!!