I want to clarify labeling I am using in my answer first. While being leftist and green is not entirely the same, green parties tend to be leftist or centre-right. Whether something is left or right, depends on the political spectrum of the society you live in. So when I single out the political right here, it is because the most vocal opposition to green policies tend to exist on the right, while leftist parties tend to also be green parties to different degrees.

The Populist Right are Against Renewable Energy

The primary reason the question about why Greens or the Left are against Nuclear power is in my experience because the populist right are trying to undermine the effort to expand renewable energy.

Climate denial is strongly linked to right wing populism. Nuclear power is more popular on the right than on the left, and often viewed as the best solution for climate change.

Right wing populists such as Donald Trump e.g. has significantly boosted investment in Nuclear Energy. This while calling climate change a hoax and vilifying renewable energy.

We see the same sentiment echoed in populist right wing media such as Breitbart. They push numerous articles presenting climate change as a hoax, while at the same time attacking the left for being against Nuclear Power.

They embrace Andrew Yang and Cory Booker e.g. for being in favor of Nuclear power as a way to fight climate change. Yet it is hypocritical to praise either one for this argument given that Breitbart believes climate change is a hoax. In other words what point is there in Nuclear power if there is no climate change going on?

Coal power is significantly cheaper than nuclear power. Nuclear is quite expensive. It would only make sense with nuclear power if you had no access to cheap coal or there is no other way to reduce CO2 emission.

This is a classic distraction tactic. Here is a great example of it with Breitbart news. Climate change is being mocked as a hoax while at the same time they are praising Mike Shellenberger, despite the fact that he is fighting climate change. So why does he get the praise? Because he is pushing nuclear power. Logically speaking this praise makes no sense given that he pushes to stop something Breitbart believes is a hoax.

However to the right wing populists Nuclear power is simply a way to attack and mock the left and undermine the effort to transition to renewable energy.

Anyone interested in this could follow Shellenberger on twitter and notice he has a huge following among climate deniers despite being an environmentalist. This is all due to this Nuclear advocacy.

Why Green Parties and the Left are Against Nuclear Power

The simple answer is that we have much better options. Nuclear power advocacy is often simply a method of derailing the debate. Nuclear power makes absolutely no sense for multiple reasons:

Solar and wind power is significantly cheaper. Solar and wind power prices drop rapidly year on year, while nuclear power prices increases or remain stagnant. Building nuclear power is very slow. It will take a long time to actually displace fossil fuel if we are building nuclear power plants. Technology development of nuclear power is very slow. New reactor designs take decades of testing and may not amount to anything. We don't have time for this. The public for good reasons doesn't like it and don't want it.

A lot of the arguments for Nuclear power is based on numerous flawed assumptions. For instance a popular argument for Nuclear advocates is how French power is significantly cheaper than German power. France of course has lots of Nuclear power while Germany is relying on renewable energy and coal.

The problem is that it is in an apples or oranges comparison. The cost of building out renewable power in Germany is factored into the electricity price. While a lot of the cost of Nuclear power in France is payed by the tax payer rather than the electricity consumer. Insuring against nuclear accidents is not included in the electricity bill, nor is the full cost of decommissioning nuclear power plants, or the risk of massive cost overruns when building new reactors.

The French energy company building and running reactors EDF is basically bankrupt and will likely need a huge taxpayer paid bailout. It has suffered huge financial blows from cost overruns of building new reactors, and it has significantly underestimated the cost of decommissioning old reactors.

Hence the price the French pay for electricity is in no way a reflection of the true cost of Nuclear power.

In fact Germany renewable energy corporations are expanding into France because they are profitable and competitive.

What About Future Modern Nuclear Reactor Designs?

There is no silver bullet in nuclear reactor design. There are almost always downsides to a design solving one issue. Pebble bed reactors for instance cannot have a nuclear meltdown by design. However in many ways they have a higher chance of causing a radioactive spill and they produce far more nuclear waste that must be treated.

Small Modular Reactors promise lower cost through mass production of smaller units. However this has never been proven nor we know if we will get the volumes that will create this price advantage. These reactors are also far less efficient and hence will consume more fuel and produce more waste.

A number of promising nuclear reactor types whether breeder reactors or thorium reactors have thus far not been demonstrated as economically viable. While we can certainly develop better design, the experience thus far has been that progress in the area simply advances very slowly.

Wind and solar power advance quickly because many units get mass produced in large factories. Nuclear power generation simply isn't mass producible in the same sense and thus you don't get the same rapid iterations and price reductions.