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Yes greenpeace, the Exxon funded anti-green terrorist organization, spread massive amounts of propaganda written by oil companies, including anti nuclear propaganda.

To your second point, nickel-iron batteries by the 1950s had developed to a point where they could compete with ice vehicles (not that they couldn't earlier as well) and would have made great electric cars and trucks given they were already the primary power source for trains (just in diesel electric form). EVs as we know them today would have been ubiquitous had Edison not been terrible with technology and science.

With that the primary use for petroleum oil would have been eliminated, and we'd need large amounts of cheap electricity by the 1950s, resulting in nuclear being the cheapest option per kWh.

You might ask why bring up green peace if I'm going a half century earlier to start this alternative history timeline... Because there was a revival of interest in EVs and alternatives to oil in the 1960s and 1970s when greenpeace was active. We could have made the switch then to EVs and nuclear plants to power them. 1970s cars were so inefficient that even the nearly century old at the time nickel iron batteries would have still been able to compete with ice engines.

But if we don't have nuclear to power them, they're not the environmentally friendly option in a time before efficient solar and wind power, so oils execs just needed to attack nuclear plants and hey, there just happens to be a group of confused hippies arguing against nuclear arms... If you could tie nuclear power to nuclear weapons and get the peace hippies convinced nuclear power leads to nuclear weapons proliferation and also convince them nuclear disasters are somehow worse than oil disasters (which even at the time was not true, it just felt that way due to biased, sponsored, media coverage) then you can convince the core audience of EVs that it's not worth investing in that tech or nuclear.

To your point in developing nations, yes they can. Foreign owned and operated nuclear plants are incredibly popular at this time, Germany's nuclear plants in Brazil being an example of nuclear being deployed to a particularly unstable developing country with minimal issues.

Minimizing uses for oil helps carve a path to eliminate it and other carbon based energy sources. Even if nuclear cannot eliminate all use in its own, it's a cornerstone technology that enables others to land the killing blow.