No, the BA pilots do not DESERVE any support, they certainly haven't supported anyone else in the past, and are very unlikely to do so in the future.
Their chosen mouthpiece, BALPA, is the most perfidious bunch ever to disgrace the co-operative movement, association, union, call it what you will. As an ex DAN captain I can vouch for this. Regrettably however, the T&Cs that they negotiate entirely for themselves do act as a benchmark and these do have an effect on the whole pilot community well-being. Galling though it may be to support them and their jackals, it is probably a necessary evil. It will be interesting to review the outcome in the future.