They don't need to be pro-nuclear in order to be green. They just can't be sitting in political debates being on the side of the table that is arguing to keeping gas, oil and coal power plants.
They just need to say: "Lets close this fossil fuel power plant".
If people then ask them about nuclear they can be just as anti-nuclear they want. They will get follow up question about what to do when energy demand exceed that of supply, but that is a separate debate between them and those arguing in favor of nuclear.
To take a example out of Swedish politics this last winter. The right movement wanted to replace an oil power plant by reopening a closed nuclear generator. The oil power plant is operating in the south of Sweden, and the plant is also the single largest contributor of green house gases in that area. To quote from memory, the green representative said "Oil power plants is a natural part of the reserve energy plan in Sweden, and there is nothing strange that it need to burn oil when demand exceed supply".
There is something broken when the highest representatives of the green movement is standing in public debates saying that oil power plants are a natural part of the grid. If that is caused by propaganda then the people who is listening need to stop doing it.
They could have said "No, lets replace that oil power plant with a green hydrogen plant". Or they could have said "No, lets replace that oil power plant with a pumped hydro storage". It would make following discussion about costs a bit more difficult, but they would still be the green movement arguing in favor of the environment. Instead they argued in favor of keeping the oil power plant running.
It really is as simple as that. No propaganda, no plot by a pro nuclear-weapons organization trying to turn the world MAD. Just politics where everything the other side say must be countered. If pro-nuclear want to close fossil fuel plants and replace them with nuclear then the anti-nuclear people want to keep the fossil fuel plants.
Keep the gas, oil and coal in the ground. It used to be slogan of the green movement. It should be again. It is a statement that both pro and anti-nuclear people could agree on if they wanted to.