I have to confess that being a fairly simple person (sic!) I don't really understand what's really behind BA taking this action against BALPA.
If they are trying to break BALPA/IFALPA financially then I think they are on a hiding to nothing in the long term. Remember that you might have to lose a battle to win the war. If the Unions do become financially broke then I am sure the pilots will be even more motivated to regroup in which case BA better watch out!
Remember Pearl Harbour - at the time a victory for the Japanese but years later USA dropped the Atom bombs on Hiroshima and Nagasaki!
At another level I find it quite heart breaking that airlines and pilots are in the current situation.