If this is illegal, the law is wrong. This has become the case in enough places that the law is losing relevance in our lives.
By what principle does a group of striking employees have some intrinsic God-given right (or right conferred by some other source of truth, outside the law) to sabotage the company that they are protesting? Is the company their property, that they have veto power over hiring? Is the labor force their property? If there is some property-like interest that grants these rights, then under what circumstances would that interest became their property rather than the original worker's? Is it strictly first come, first serve? Is there a vesting period during which this right accrues? Are the striking employees as a group to be considered a form of government, that they may regulate hiring and firing? What elevates this right or interest over other cherished principles, such as free association? Or do the strikers simply wish to subjugate such principles to serve their own self-interest?
I believe that you propose mob rule. It is no surprise, then, that you are in conflict with a nation ruled by laws, rather than by mobs and strongmen.
It isn't? In many parts of the US a car is needed to hold a job, or to even get to the grocery store (which might be miles away). Moreover, grocery stores do provide the means to "feed your family". Does that mean looting/vandalizing them is fair game after failing to "negotiate" with them?
If you have somehow gotten yourself into a position where you are supporting a family based on knowing how to do one thing that you can only do for one company, sorry but you either massive screwed up your life (unlikely) or you are afraid to step outside your comfort zone and work elsewhere (likely).