If the union you belong to goes out on strike, you do have the right to work during the strike. However, you should proceed very cautiously. Here’s why:
If you are a union member, while you do have the right to work during a strike, most unions have rules that prohibit their members from crossing a picket line and working through a strike, or engaging in any activity that is in conflict with the members’ responsibility toward the union.
As a result, if you engage in this type of activity as a union member, the union has the legal right to place you on trial.
If you are found guilty at a union trial, the union could fine you money and take you to court if you refuse to pay the fine.
According to the National Right To Work Legal Defense Foundation, in the private sector…
If you want to work during a strike you must be certain that you are not a union member if you wish to avoid union discipline.
Many courts have held that unions have the power to discipline their members. This discipline can include imposing a significant fine upon and then suing you to enforce the payment of the fine. If you wish to avoid consequences like that, you cannot remain a member of the union and cross the picket line.
To read more about your rights during a strike, go here.