Having worked in BACX a few years ago and seen the bickering between mainline and CX company councils and pilots, I reckon in reality there will be no support across the companies.
However, I do feel that it is shameful if there is no support. There is such a misunderstanding between the two companies, as demonstrated by the article and letters in the Log recently.
We are both a group of pilots who are doing our jobs well, its not like BA are amazing and BACX are not, which unfortunatlely is the attitude of a voiciforous few. The ones who do know BACX are a good bunch are too quiet about it, and in reality not many BA pilots understand who or what BACX is. There is still much confusion between City Flyer and CitiExpress. when people ask me my background, they often say they understand and then ask if I was based at LGW on the RJ - wrong company!
Anyhow, I reckon BALPA should be encouraging us to work together and understand each others situations, that is something they are terrible at.