'The travelling public doesn't give a damn.' - and therein lies the problem with the current state of the airline industry. You, the travelling public, has been given all-time low airline fares combined with all-time low standards; and you lap it up. But that has come at the expense (BA and legacy carriers' crews excluded who through sheer 'muscle' have been able to defend their positions) at an erosion of pay and terms and conditions among a very large number of professional pilots over the past 10 years. This assault has been lead by the likes of O'Leary and now Walsh (there is a common factor here) and it is time that it is made quite clear that enough is enough. If it means putting £10 on a seat then so be it.
In my opinion BA crew do not have to get the public 'on side'. It is an internal dispute but the only way in which such disputes hit home is when the shareholders' bottom-line is hit. And have no worries, this will not bring BA down - Irish upstarts might.