Prior to the adoption of containers, the industries of a given region were heavily dependent upon a nearby port. When that port was shut down by a strike, those industries quickly lost the ability to acquire supplies and export products. Containers made the industries of a region less dependent upon any given port. Thus, a strike in any given port would only result in a shift of traffic to another port. To put things another way, the advent of the container in some ports deprived organized labor of its chief means of opposing the adoption of containerization in others.
This meant that any union-led campaign against containerization would have to have been extraordinarily broad-based, involving either coordinated work stoppages along the entirety of a seacoast or work stoppages involving railroad workers and truck drivers as well as longshoremen. Such large-scale action would have required either a labor movement that was strong in all of the ports of a given seacoast or a labor movement that could coordinate the actions of several different unions.
In short, in order to delay containerization, one needs to have a labor movement that was quite different from the labor movements of the 1960s of our own time line.