How have military and societal needs impacted the education of engineers since the start of the 20th century?

Engineering is a very practical field, much more so than say art history or classical literature. This doesn't necessarily make it more important, but it does tend to make it more responsive to changes in politics and culture.

War often drives the training of engineers, because modern warfare requires many skilled engineers to build more and better war machines---tanks, ships, airplanes, guns, missiles. The World Wars especially created a huge demand for skilled engineers, and also for scientists as well, particularly physicists and chemists. It is often argued that physicists won WW2, by developing the atom bomb; but in fact military engineers of all sorts were vital to the success of the war effort.

After WW2, the world entered a period of peace, but initially this peace was overshadowed by the constant threat of nuclear war---the Cold War. Perhaps because of how important science and technology had been in WW2, in the Cold War both the US and the USSR dramatically increased their investment in STEM (science, technology, engineering, and mathematics) education and research. Part of their goal was to invent better war machines before the other side could; part of it was a more general sense that technological superiority (such as the Space Race) would prove the superiority of their economic ideology (capitalism and Communism respectively). This increased investment was very expensive, but also had many long-run benefits, contributing to the rise of transistors, computers, and the Internet later on.

Now that the USSR has collapsed and the Cold War is over, investment in STEM has been somewhat rolled back, but only partially. People saw the large civilian benefits of heavy STEM investment, and sought to preserve them. One of the primary goals of the various educational reforms that are often implemented is usually to improve outcomes in STEM and make more people into scientists and engineers. While during the Cold War that education was expressly focused on inventing better military technology than the opposing side, today it has broader goals, often aiming for improvements in innovation and economic prosperity more generally. This has likely been influenced by the meteoric success of a handful of multi-billionaire computer engineers in the 1990s Web boom, such as Bill Gates and Steve Wozniack. Where previously we trained engineers with the goal of beating the Soviet Union, now we train them with the goal of making the next Bill Gates. (Whether this will actually work remains to be seen.)