Dealing with the instability of solar and wind energy is very complex and requires numerous measures, such as better integration of wide-area electricity grids, more electricity storage, more generation reserves, etc.
But even nuclear power generation is dependent on the weather. During heat waves, nuclear power plants located on rivers in Germany and France repeatedly had to shut down because there was not enough cooling water available or the water in the rivers would otherwise have become too warm.[1] During cold spells, nuclear power plants had sometimes to be shut down because the supply of cooling water was no longer guaranteed due to ice.[2]
[1] For example: https://www.reuters.com/article/us-france-electricity-heatwa...
[2] For example: https://fortune.com/2019/01/31/ice-shutdown-new-jersey-nucle...