Water vapor released by nuclear power plants worsens climate change
False !
In brief
In detail

The white plumes emerging from cooling towers have undeniably become the symbol of nuclear power in the collective imagination. Yet these plumes are nothing but water vapor.
Too short a stay to make an impact
As water vapor is a powerful greenhouse gas, it is legitimate to ask how these releases effect our environment. However, the capacity of air to contain water vapor is limited. In the lower atmosphere, the water vapor concentration is close to the saturation level and any additional water vapor ends up recondensing. Anecdotally, a molecule of water stays in the atmosphere for only two weeks, on average. This stay is far too short for the water vapor produced by nuclear power plants to have any impact on global warming.
Water vapor and global warming
But then, why do we often hear about the impact of water vapor on global warming?
The key to understanding this is the feedback mechanism. Any increase in temperature at the Earth's surface increases the permissible concentration of water vapor in the air, an increase in concentration which, in turn, contributes to the rise in temperature. It is important to note that the situation is very different in the upper atmosphere: as the air is not saturated with water vapor, additional vapor does not condense. This is one of the mechanisms of aviation's contribution to climate change.
Sources:
[1] Vapeur d’eau et réchauffement climatique, François-Marie Bréon (climate scientist), https://theconversation.com/oui-la-vapeur-deau-est-un-gaz-a-effet-de-serre-et-a-un-impact-sur-le-rechauffement-climatique-199017