You are accusing environmental organizations of not believing in climate change as a debating tactic. That is uncharitable! But also just weird.

Just leave that part out, it only detracts from your message.

"I think environmental orgs should support nuclear as it is low carbon and generally aligned with their goals. I'm disappointed that many of their members seem to be unaware of the true record on plant safety, particularly compared with coal"

Adding anything about them not believing in climate change makes it sound like you are repeating talking points you picked up from fossil fuel funded propagandists, who to this day are pushing that message.

(Your opinions on nuclear also reveal that media diet, but in a much more subtle way).