The concern is not that people will start dropping like flies, it's that the changing climate will have destabilizing effects on the economy, geopolitics, and the ecosystem. For example, drought contributed to the Syrian conflict, the rise of ISIS, etc: https://www.pnas.org/doi/10.1073/pnas.1421533112

If individual citizens can affect their local politics to mitigate climate change, it is important to do so.