“In the vast majority of important political decisions I see that the politicians follow the changes in the society—they rarely lead them [...].”
This is a widely-expressed sentiment, but I think it is not true. There are many examples of politicians taking (often momentous) decisions which are out of step with public opinion. E.g:
UK politicians abolishing the death penalty in 1965, despite clear public opposition. (https://www.bbc.co.uk/news/uk-32061822)
The UK government hitting the 0.7% aid target for many years, despite opinion polling showing that a majority of the public opposed this
Tony Blair taking the decision to commit British troops to the invasion of Iraq in 2003, despite widespread public opposition (https://www.theguardian.com/politics/2003/jan/21/uk.iraq2)
(More extremely, and in a very different context, Adolf Hitler abolishing liberal democracy having won just 33pc of the vote in the November 1932 elections.)
The idea that politicians merely follow broader societal trends and public opinion is not true. They often act counter to these trends. And they often, themselves, help to shape these trends (eg, perhaps, civil partnerships and same-sex marriage in the UK).
There is plenty of space for politicians to take high-stakes decisions based on their own conscience and values—decisions which often lead or even defy public opinion. For good or ill, politics offers leverage for impact-minded individuals.
The ‘Effective Manager’ book you mention looks awesome. I’d also very highly recommend this book, focussed on all aspects of general non-profit management: Managing to Change The World, by Alison Green—https://www.amazon.co.uk/Managing-Change-World-Nonprofit-Managers/dp/1118137612