Climate change is an immediate existential threat as you say yourself. Seeing nuclear as the solution to that threat is very shortsighted IMHO.
Many commenters mention the threat of accidents like Chernobyl or Fukushima. That is one aspect, yes. However, on the grand scale it seems as if humanity has limited the risk for these kind of accidents.
The much bigger problem with nuclear energy is that humanity has not yet figured out how to handle the waste on the short term. Let alone on a time scale that is beyond human comprehension.
I was quite impressed by the thorough analysis in this article:
https://bostonreview.net/articles/is-nuclear-power-our-best-...
Piling more nuclear waste on to the already unmanageable heap is irresponsible. That is why being against nuclear energy as the stop gap solution for climate change is not only reasonable but also responsible.