"They say nuclear power is a non-renewable fuel that will run out in about a century, and that it generates greenhouse gases in the mining, processing and transportation that true renewable energy sources such as solar and wind power do not."

It is clear that they haven't even considered the most common fuel for a nuclear reactor on earth, Thorium, which had a several thousand year supply. Uranium-238, also an energy source already being used in a handful of reactors on earth, has a several thousand year supply. Sure we might run out of Uranium-235 in a hundred years but that is hardly the end of the age of nuclear reactors.

Claiming that wind turbines and solar panels do not generate greenhouse gases in the mining, processing and transportation is also ridiculous. If you take account of the low capacity factor, it takes about 3000 1.5 MW turbines to produce as much electricity as one nuclear reactor. Each of these turbines uses a huge amount of material that must be mined out of the earth than transported to the site by a truck and assembled by crane that operates off of fossil fuels. Whenever decent lifetime calculations have been done comparing the CO2 emissions of wind and nuclear they come out about the same. This means a reasonable plan to cut greenhouse emissions would be producing both wind turbines and nuclear power plants just as fast as we can.

Claiming that nuclear waste is a reason to stop the production of nuclear power plants is also ridiculous. The nuclear power industry in America has operated more than a hundred reactors and has never killed a single member of the public from a release of radiation. Compared to the thousands a year that get killed from particulate and mercury pollution from coal plants this is an amazing record. Even in the unlikely event we were to have a Chernobyl in America every thirty years nuclear reactors would be incapable of killing even a tenth of the number of people coal does.