For many workers, the membership card mattered less than the struggle, and they did not hesitate to strike even if they were not members of the unions that called the strike.
This is common in Italy. A minor part of the workforce is part of a union (our unions are different from what an American might be used to, btw), mainly because membership has a cost (usually ~1% of your wages), and because many are afraid of what employers may think when they find out.
Non-members still regularly join strikes and protests when they care about the subjects.