If, as Miss M states, that this offer is totally unacceptable to the BASSAnistas then there is the option for them to leave the airline and find another job with their requirements
The problem for the majority of the hardcore is that they have no viable alternative form of employment. Certainly there is no form of employment available to the majority that will be pay as much with as much time off and other favourable T&Cs as they have at BA. Despite the protestations of being highly qualified etc, the majority of CC have been in BA for a long time and their alternative skill sets are out of date.
This leads the reasoning behind the "I will strike until I get what I want or BA goes bust" mentality. It is for many their only option - if they see a major reduction in their T&Cs they may as well risk the bankruptcy and dissolution of BA, as the option of leaving would lead to a major reduction in their T&Cs. The end result for them is the same - hence the vehemence of their rhetoric.