Because of the late usage of nuclear weapons, they aren't seen as Doomsday weapons for some reason despite fall out existing here. Plus there is no taboo on nuclear energy for TTL.
Perhaps more importantly, the A4's locking up of middle east oil fields will likely have meant there was no equivalent of the 1973 oil crisis: counter-intuitive as it sounds that crisis was actually
bad for nuclear energy.
The crisis triggered conservation measures which reduced demand for energy (causing many nuclear power projects to be cancelled, as they were predicated on much higher levels of forecast energy use) and also resulted in a decade of high interest rates (to control the inflation caused by high oil prices, and which also disproportionately hurt nuclear with its very front-loaded costs) which was in turn followed by a couple of decades of low natural gas prices which nuclear couldn't compete with.
And as for public opinion turning against nuclear power, wasn't that at least in part because ratepayers came to associate nuclear power with rising prices (perhaps because the costs of servicing debts taken to build nuclear plants had increased so much that utilities were forced to pass them on to the consumer), rather than because of the "classic" anti-nuclear arguments?