While there clearly was some connection between the energy crisis of the 1970s and the rise of the environmental movement, it would not really be right to say that the crisis caused the movement to arise. Instead, the movement was already in existence and the energy crisis helped to strengthen it.
We can prove the fact that the energy crisis did not bring the movement about simply by looking at the chronology of the environmental movement. For example, the Environmental Protection Agency (EPA) was created in 1969. The first Earth Day was celebrated the next year. The Clean Air Act was passed into law in 1970 while the Clean Water Act became law in 1972. By contrast, the first major event of the energy did not come until 1973. This shows us that the energy crisis could not possibly have caused the environmental movement to come into existence.
However, we can say that the energy crisis helped to strengthen the movement. It helped to convince people, at least to some degree, that it was important to conserve energy. Therefore, the energy crisis did have some impact on the environmental movement.