Other pollutants (e.g. nuclear wastes) are (of course) a concern. However, right now, we face an existential threat from the atmospheric levels of carbon emissions.
The accumulation of nuclear wastes is a very real problem, however, it does not represent an immediate threat, and, frankly, is a localized threat. There are various schemes to deal with it, but none of them will matter if we are all dead.
https://www.theguardian.com/environment/2015/dec/03/nuclear-power-paves-the-only-viable-path-forward-on-climate-change
Nuclear power, particularly next-generation nuclear power with a closed fuel cycle (where spent fuel is reprocessed), is uniquely scalable, and environmentally advantageous. Over the past 50 years, nuclear power stations by offsetting fossil fuel combustion have avoided the emission of an estimated 60bn tonnes of carbon dioxide. Nuclear energy can power whole civilisations, and produce waste streams that are trivial compared to the waste produced by fossil fuel combustion. There are technical means to dispose of this small amount of waste safely. However, nuclear does pose unique safety and proliferation concerns that must be addressed with strong and binding international standards and safeguards. Most importantly for climate, nuclear produces no CO₂ during power generation.