Do employees who pay union dues and are union members have a different obligation than non-members to support a strike called or supported by the union that represents them? Can the union member be penalized for not striking?

No employee is ever under any obligation to strike. Unions are legally prohibited from threatening or coercing members in other ways to keep them from coming to work. However, some unions have the right to levy fines against members, but not agency fee payers, who choose to work during a strike, including a sympathy strike. The employee needs to contact her/his local union representative regarding possible penalties for union members not striking.