Ignoring the typical arguments against nuclear, I think a main point from them specifically is that investment in energy is zero-sum, and state resources directed towards nuclear energy are resources not going towards renewable energies. Furthermore, heating and transport make up a large proportion of carbon emissions, and these generally aren't powered by nuclear energy. So nuclear places the focus of energy transformation in the wrong place, and allows governments to believe they are solving the problem when much larger investment in renewables is required.
I'm not qualified enough in the area to agree or disagree with the implicit tradeoffs there, it's just the argument I've heard.