Actually, there is a lot of overlap between opponents of hydropower, nuclear energy, and nuclear weapons. This overview isn't as brief as I had first planned, and it touches on some other issues as well, but it shows quite a few of the factors that worked against hydropower and nuclear energy.
The environmentalist movement in the United States was originally started by opponents of dam development. If you go back to when the Sierra Club and similar groups were started, they were actually backed by more conservative conservationist types who wanted to preserve the wilderness for hunting, fishing, recreation, etc.
In the 1960s the Sierra Club had a new head who was personally opposed to nuclear power, and made his goals those of the organization. This was not without controversy, as the organization had previously agreed to remain neutral regarding nuclear power and other energy issues, focusing just on dams, wildlife, etc.
In 1968 the National Environmental Protection Act was passed, and for a few years it was unclear if it applied to the Atomic Energy Commission, which was one of the most powerful organizations in the United States at the time, backed by the very powerful Joint Committee on Atomic Energy in the United States Congress. In the Calvert Cliffs Decision it was determined that NEPA did apply, so the AEC had to go back and do an environmental review on all civilian nuclear energy facilities planned, building, and even already completed.
There was also an increasing focus on safety, as the AEC realized that the passive safety capabilities of the 100 megawatt type reactors the standards were developed for back in the 1950s were totally inadequate for the emerging gigawatt class super-reactors being ordered by the 1970s. The changing standards and constant requirements for retrofits, modifications, etc. led to escalating costs at facilities being planned and built, and major expenditures to bring existing plants up to code. Things like cooling towers, emergency coolant systems, etc. had to be added at tens to hundreds of millions of dollars, with cooling tower retrofits costing almost as much as the total cost to build some of the mid-1960s facilities. At least one early reactor was decommissioned due to the expense of retrofits.
Similar things happened with hydropower facilities, as they had to be redesigned or modified to provide protection to aquatic life. Spill water, which is diverted over the top of the dam rather than through the turbines (for high water conditions, low power conditions, etc.), also became regulated as an effluent under the Clean Water Act, as the water accumulates gasses as it falls over the dam that result in harmful gas buildup in the river once it lands. The fish can actually get the bends from spill water if it isn't carefully spilled.
All of this led to escalating costs at nuclear and hydropower facilities, but especially nuclear facilities. This is largely because all the good hydropower locations in the United States had already been built by the 1970s, so there wasn't as much impact to be had. Nuclear was heavily impacted because of the changing standards, the long construction times (longer in some cases than hydropower facilities), the shifting standards for designs and the one-off design of every nuclear plant every built in the United States (each plant is essentially totally unique), and the collapse in energy demand following the crises.
The final factor that worked against nuclear energy was its association with nuclear weapons. The dream of the AEC scientists had always been to develop the fast breeder reactor and nuclear reprocessing, which would allow for an essentially limitless supply of atomic energy. Breeder reactors turn thorium and nuclear waste into usable fuel, which lead some scientists to compare them to perpetual energy machines. They still need fuel, but at current consumption levels there is billions of years of material available if breeder reactor and reprocessing technology is used. The major issue with this for anti-nuclear weapons advocates is that breeder reactors can also produce vast quantities of material suitable for nuclear weapons. Because reprocessing is vital to the entire breeder reactor plan, the materials would be extracted from the fuel as general practice, as opposed to remaining in the spent fuel rods and being disposed with them.
All these factors combined meant that 1978 was the year the last nuclear reactor was ordered in the United States. Public support for nuclear energy had also already started to trend negative by the mid to late 1970s, with public support for having a nuclear reactor built near them being more opposed than favorable by the late 1970s. Interestingly, this occurred prior to Three Mile Island, and prior to the Second Energy Crisis of 1979.